Publications
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R. T. Rockafellar's home page

Progressive decoupling of linkages in optimization and variational
inequalities with elicitable convexity or monotonicity
Setvalued and Variational Analysis, accepted
(by R. T. Rockafellar).

Variational convexity and the local monotonicity of subgradient mappings
Vietnam Journal of Mathematics, submitted 2018
(by R. T. Rockafellar).

Risk and utility in the duality framework of convex analysis
From Analysis to Visualization: a Celebration of the Life and Legacy of
Jonathan M.\ Borwein, Springer Proceedings in Mahematics and Statistics, to
appear
(by R. T. Rockafellar).

Minimizing buffered probability of exceedance by progressive hedging
Mathematical Programming B, submitted 2018
(by R. T. Rockafellar and S. Uryasev).

Solving Lagrangian variational inequalities with applications to
stochastic programming
Mathematical Programming B, submitted 2018
(by R. T. Rockafellar and J. Sun).

Progressive decoupling of linkages in monotone variational inequalities
and convex optimization, submitted 2017
(by R. T. Rockafellar).

On the stability and evolution of economic equilibrium,
Economic Theory, submitted 2017
(by A. Jofr\'e, R. T. Rockafellar and R. JB Wets).

Radius theorems for monotone mappings, Setvalued and Variational
Analysis, submitted 2017
(by A. D. Dontchev, A. Eberhard and R. T. Rockafellar).

Variational analysis of Nash equilibrium, Vietnamese Journal of
Mathematics, accepted 2017
(by R. T. Rockafellar).

Problem decomposition in blockseparable convex optimization: Ideas old
and new, Journal of Nonlinear and Convex Analysis 19 (2018)
(by R. T. Rockafellar).

Solving monotone stochastic variational inequalities and complementarity
problems by progressive hedging,
Mathematical Programming B, accepted 2017
(by R. T. Rockafellar and Jie Sun).

Solving stochastic programming problems with risk measures by progressive
hedging, SetValued and Variational Analysis 26 (2018), 759768
(by R. T. Rockafellar).

Superquantile/CVaR risk measures: secondorder theory,
Annals of Operations Research 262 (2018), 329
(by R. T. Rockafellar and J. O. Royset).

Convexity and reliability in engineering optimization,
Proceedings of Conference on Nonlinear Analysis and Convex Analysis
(Chiang Rai, Thailand, 2015), 110
(by R. T. Rockafellar).

Stochastic variational inequalities: singlestage to multistage,
Mathematical Programming B, accepted 2016
(by R. T. Rockafellar and R. JB Wets).

Importance sampling in the evaluation and optimization of buffered
failure probability,
Proceedings 12th International Conference on Applications of Statistics
and Probability in Civil Engineering (ICASP), Vancouver (2015)
(by M. M. Harajli, R. T. Rockafellar and J. O. Royset).

Measures of residual risk with connections to regression, risk tracking,
surrogate models and ambiguity, SIAM Journal on Optimization
(by R. T. Rockafellar and J. O. Royset).

Risk measures in engineering design under uncertainty,
Proceedings 12th International Conference on Applications of Statistics
and Probability in Civil Engineering (ICASP), Vancouver (2015)
(by R. T. Rockafellar and J. O. Royset).

IMPLICIT FUNCTIONS AND SOLUTION MAPPINGS,
second edition. Springer Series in Operations Research and Financial
Engineering, 2014 [466 pages]
(by A. L. Dontchev and R. T. Rockafellar).

Secondorder variational analysis and its role in optimization,
Proceedings of NACA2013
(by R. T. Rockafellar).

The convex analysis of random variables,
Proceedings of the Third Asian Conference on Nonlinear Analysis and
Optimization (Matsue, Japan, 2012): Yokohama Publishers, 2014: 277286
(by R. T. Rockafellar).

Engineering decisions under riskaverseness, Journal of Risk and
Uncertainty in Engineering Systems
(by R. T. Rockafellar and J. O. Royset).

Superquantiles and their applications to risk random variables and
regression,
Tutorials in Operations Research INFORMS 2013, 151167
(by R. T. Rockafellar and J. O. Royset).

Full stability in finitedimensional optimization,
Math. of Operations Research, accepted
(by B. S. Mordukhovich, T. T. A. Nghia and R. T. Rockafellar).

Convex analysis and financial equilibrium,
Mathematical Programming B 148 (2014), 223240
(by A. Jofre, R. T. Rockafellar and R. JB Wets).

Superquantile regression with applications to buffered reliability,
uncertainty quantification and conditional valueatrisk,
European J. Operations Research 234 (2014), 140154
(by R. T. Rockafellar, J. O. Royset and S. I. Miranda).

Random variables, monotone relations and convex analysis,
Mathematical Programming B 148 (2014), 297331
(by R. T. Rockafellar and J. O. Royset).

Characterizations of full stability in constrained optimization,
SIAM J. Optimization 23 (2013), 18101849.
(by B. S. Mordukhovich, R. T. Rockafellar, and M. E. Sarabi).

Convexconcaveconvex distributions in application to CDO pricing,
Computational Management Science (2013), 124
(by V. Veremyev, P. Tsyurmasto, S. Uryasev, R. T. Rockafellar).

Direct proof of the shift stability of equilibrium in classical
circumstances, Economics Letters, submitted
(by A. Jofre, R. T. Rockafellar and R. JB Wets).

An EulerNewton continuation method for tracking solution trajectories of
parametric variational inequalities,
SIAM J. Control and Optimization 51 (2013), 18231840
(by A. D. Dontchev, M. Krastanov, R. T. Rockafellar and V. Veliov).

Applications of convex variational analysis to Nash equilibrium,
Proceedings of 7th International Conference on Nonlinear Analysis and
Convex Analysis (Busan, Korea, 2011) II, 173183
(by R. T. Rockafellar).

Secondorder subdifferential calculus with applications to tilt stability
in optimization, SIAM Journal on Optimization 22 (2012), 953986
(by B. S. Mordukhovich and R. T. Rockafellar).

The robust stability of every equilibrium in economic models of exchange
even under relaxed standard conditions,
submitted
(by A. Jofre, R. T. Rockafellar and R. JB Wets).

The fundamental risk quadrangle in risk management, optimization and
statistical estimation,
Surveys in Operations Research and Management Science 18 (2013), 3353
(by S. Uryasev and R. T. Rockafellar).

Calibrating risk preferences with generalized CAPM based on mixed CVaR
deviation, Journal of Risk 15 (2012), 4570
(by K. Kalinchenko, S. Uryasev and R. T. Rockafellar).

Convergence of inexact Newton methods for generalized equations,
Mathematical Programming B 139 (2013), 115137
(by A. L. Dontchev and R. T. Rockafellar).

Parametric stability of solutions to problems of economic equilibrium,
Convex Analysis 19 (2012), No. 4
(by A. L. Dontchev and R. T. Rockafellar).

A computational study of buffered failure probability in reliabilitybased
optimization, Proceedings of the 11th International Conference on
Application of Statistics and Probability in Civil Engineering, Zurich,
Switzerland, 2011
(by H. G. Basova, R. T. Rockafellar and J. O. Royset).

General economic equilibrium with financial markets and retainability,
submitted
(by A. Jofre, R. T. Rockafellar and R. JB Wets).

A timeembedded approach to economic equilibrium with incomplete markets,
Advances in Mathematical Economics 14 (2011), 183196
(by A. Jofre, R. T. Rockafellar and R. JB Wets).

On buffered failure probability in design and optimization of structures,
J. Reliability Engineering and System Safety 95 (2010), 499510
(by R. T. Rockafellar and J. O. Royset).

A calculus of proxregularity, J. Convex Analysis 17 (2010), 203210
(by R. A. Poliquin and R. T. Rockafellar).

Saddle points of Hamiltonian trajectories in mathematical economics,
Control and Cybernetics 4 (2009), 15751588
(by R. T. Rockafellar).

IMPLICIT FUNCTIONS AND SOLUTION MAPPINGS,
Monographs in Mathematics, SpringerVerlag, 2009 [375 pages]
(by A. L. Dontchev and R. T. Rockafellar).

Newton's method for generalized equations: a sequential implicit function
theorem, Mathematical Programming (Ser. B) 123 (2010), 139159
(by A. L. Dontchev and R. T. Rockafellar)

Coherent approaches to risk in optimization under uncertainty,
Tutorials in Operations Research INFORMS 2007, 3861
(by R. T. Rockafellar)

Risk tuning with generalized linear regression,
Mathematics of Operations Research (2008)
(by R. T. Rockafellar, S. Uryasev and M. Zabarankin)

Linearconvex control and duality,
Advances in Mathematics for Applied Sciences 76 (2008), 280299
(by R. Goebel and R. T. Rockafellar)

Local strong convexity and local Lipschitz continuity of the gradients of
convex functions, J. Convex Analysis 15 (2008), 263270
(by R. Goebel and R. T. Rockafellar).

Parametrically robust optimality in nonlinear programming,
Applied and Computational Math. 6 (2006), 5965
(by A. L. Dontchev and R. T. Rockafellar)

Robinson's implicit function theorem and its extensions,
Mathematical Programming (Ser. B) 117 (2009), 129147
(by A. L. Dontchev and R. T. Rockafellar)

Equilibrium with investors using a diversity of deviation measures,
J. Banking and Finance 31 (2007), 32513268
(by R. T. Rockafellar, S. Uryasev and M. Zabarankin)

Variational inequalities and economic equilibrium , Math. of Operations
Research 32 (2007), 3250
(by A. Jofre', R. T. Rockafellar and R. JB Wets)

Optimality conditions in portfolio analysis with general deviation
measures , Mathematical Programming Ser. B. 108 (2006), 515540
(by R. T. Rockafellar, S. Uryasev and M. Zabarankin)

Moreau's proximal mappings and convexity in HamiltonJacobi theory,
in [196], 312 (by R. T. Rockafellar)

NONSMOOTH MECHANICS AND ANALYSIS: THEORETICAL AND NUMERICAL ADVANCES,
edited conference book (P. Alart, O. Maisonneuve and R. T. Rockafellar),
SpringerVerlag, 2005.

Master funds in portfolio analysis with general deviation measures,
J. Banking and Finance 30 (2005), 743778
(by R. T. Rockafellar, S. Uryasev and M. Zabarankin)

A variational inequality scheme for determining an economic equilibrium of
classical or extended type,
in Variational Analysis and Applications (F. Giannessi and A. Maugeri,
eds.), Springer, 2005, 553578 (by A. Jofre', R. T. Rockafellar and
R. JB Wets)

HamiltonJacobi theory and parametric analysis in fully convex problems of
optimal control, J. Global Optimization 28 (2004), 419431 (by R. T.
Rockafellar)

Generalized deviations in risk analysis,
Finance and Stochastics 10 (2006), 5174
(by R. T. Rockafellar, S. Uryasev and M. Zabarankin)

Regularity properties and conditioning in variational analysis and
optimization, SetValued Analysis 12 (2004), 79109
(by A. L. Dontchev and R. T. Rockafellar)

A property of piecewise smooth functions,
Comput. Optim. Appl. 25 (2003), 247250 (by R. T. Rockafellar)

Envelope representations in HamiltonJacobi theory for fully convex problems of
control, Proceedings 40th IEEE Conf. on Decisions and Control (Orlando,
Florida), 27682771 (by R. T. Rockafellar and P. R. Wolenski)

Duality and dynamics in HamiltonJacobi theory for fully convex problems of
control, Proceedings 40th IEEE Conf. on Decisions and Control (Orlando,
Florida), 27632767 (by R. T. Rockafellar and P. R. Wolenski)

Conditional valueatrisk for general loss distributions,
J. Banking and Finance 26 (2002), 14431471

Variational Geometry and equilibrium, in Nonconvex Optimization and its
Applications (P. Daniele, F. Giannessi and A. Maugeri, eds.), Kluwer, 2003
(by M. Patriksson and R. T. Rockafellar)

Convex analysis in the calculus of variations, in Advances in Convex
Analysis and Global Optimization (N. Hadjisavvas and P. M. Pardalos, eds),
Kluwer, 2001, 135152 (by R. T. Rockafellar)

Sensitity analysis of aggregated variational inequality problems,
with application to traffic equilibria,
Transportation Science 37 (2003), 5668 (by M. Patriksson and R. T.
Rockafellar)

Generalized conjugacy in HamiltonJacobi theory for fully convex
Lagrangians,
J. Convex Analysis 9 (2002), 463474 (by R. Goebel and R. T. Rockafellar)

A mathematical model and descent algorithm for bilevel traffic management,
Transportation Science 36 (2002), 271291 (by M. Patriksson and R. T.
Rockafellar)

Graphical convergence of sums of monotone mappings,
Proc. Amer. Math. Soc. 130 (2002), 22612269 (by T. Pennanen,
R. T. Rockafellar and M. Théra).

The radius of metric regularity,
Trans. Amer. Math. Soc. 355 (2003), 493517
(by A. L. Dontchev, A. S. Lewis and R. T. Rockafellar)

Optimization of conditional valueatrisk, Journal of Risk 2 (2000),
493517 (by R. T. Rockafellar and S. Uryasev)

Primaldual solution perturbations in convex optimization,
SetValued Analysis 9 (2001), 4965 (by A. L. Dontchev and R. T.
Rockafellar)

Ample parameterization of variational inclusions,
SIAM J. Optimization 12 (2002), 170187 (by A. L. Dontchev and
R. T. Rockafellar)

Secondorder convex analsis,
J. Nonlinear and Convex Analysis 1 (1999), 116 (by R. T. Rockafellar)

Extended nonlinear programming, in Nonlinear Optimization and Related
Topics (G. Di Pillo and F. Giannessi, eds.), Kluwer, 1999, 381399

Stability of locally optimal solutions,
SIAM J. Optimization 10 (2000), 580604 (by A. B. Levy, R. A. Poliquin and
R. T. Rockafellar)

Duality and optimality in multistage stochastic programming,
Annals of Operations Research 85 (1999), 119 (by R. T. Rockafellar)

Convexity in HamiltonJacobi theory 2: envelope representations,
SIAM J. Control Opt. 40 (2001) 13511372 (by R. T. Rockafellar and
P. R. Wolenski)

Convexity in HamiltonJacobi theory 1: dynamics and duality,
SIAM J. Control Opt. 40 (2001) 13231350 (by R. T. Rockafellar and
P. R. Wolenski)

Local differentiability of distance functions,
Trans. Amer. Math. Soc. 352 (2000), 52315241 (by R. A. Poliquin,
R. T. Rockafellar and L. Thibault)

VARIATIONAL ANALYSIS, Grundlehren der Mathematischen Wissenschaften 317,
SpringerVerlag 1997 (733 pages) (by R. T. Rockafellar and R. JB Wets).
Second printing 2004, third printing 2009. Corrections/additions:
to the first (incorporated in the second),
to the second (incorporated in the third),
and to the third (ongoing)

Protoderivatives of partial subgradient mapping
J. Convex Analysis 4 (1997), 221234 (by R. A. Poliquin and R. T. Rockafellar)

Tilt stability of a local minimum,
SIAM J. Optim., 8 (1998), 287299 (by R. A. Poliquin and R. T. Rockafellar)

Characterizations of lipschitzian stability in nonlinear
programming,
in Mathematical Programming With Data Perturbations
(A. V. Fiacco, ed.), Marcel Dekker, New York, 1997, 6582 (by A.
Dontchev and R. T. Rockafellar).

A derivativecoderivative inclusion in secondorder nonsmooth
analysis, SetValued Analysis 5 (1997), 117 (by R. T. Rockafellar
and D. Zagrodny)

Bolza problems with general time constraints, SIAM J.
Control Opt. 35 [1997], 20502069 (by P. D. Loewen and R. T. Rockafellar)

Protoderivatives and the geometry of solution mappings in nonlinear
programming, in Nonlinear Optimization and Applications (G. Di
Pillo and F. Giannessi, eds.), Plenum, New York, 1996, 249260 (by A.
Levy and R. T. Rockafellar)

Convergence rates in forwardbackward splitting, SIAM J.
Optim. 7 (1997), 421444 (by G. H.G. Chen and R. T. Rockafellar)

Characterizations of strong regularity for variational inequalities
over polyhedral convex sets, SIAM J. Optim. 6 (1996),
10871105 (by A. L. Dontchev and R. T. Rockafellar)

Secondorder nonsmooth analysis in nonlinear programming,
in Recent Advances in Optimization (D. Du, L. Qi and R. Womersley,
eds.), World Scientific Publishers, 1995, 322350 (by R. A. Poliquin
and R. T. Rockafellar)

Sensitivity of solutions in nonlinear programming problems with
nonunique multipliers, in Recent Advances in Optimization (D. Du,
L. Qi and R. Womersley, eds.), World Scientific Publishers, 1995, 215223
(by A. B. Levy and R. T. Rockafellar)

Generalized Hessian properties of regularized nonsmooth functions,
SIAM J. Optim. 6 (1996), 11211137 (by R. A. Poliquin and R. T.
Rockafellar)

Proxregular functions in variational analysis,
Trans. Amer. Math. Soc. 348 (1996), 18051838 (by R. A. Poliquin and
R. T. Rockafellar)

New necessary conditions for the generalized problem of Bolza,
SIAM J. Control Opt. 34 (1996), 14961511 (by P. D. Loewen and
R. T. Rockafellar)

Equivalent subgradient versions of Hamiltonian and EulerLagrange
equations in variational analysis, SIAM J. Control Opt. 34
(1996), 13001315 (by R. T. Rockafellar

Monotone relations and network equilibrium, in Variational
Inequalities and Network Equilibrium Problems (F. Giannessi and A.
Maugeri, eds.), Plenum, London, 1994, 271288 (by R. T. Rockafellar)

Nonsmooth optimization, in Mathematical Programming: The State of
the Art 1994 (J. R. Birge and K. G. Murty, eds.), Univ. of Michigan
Press, 1994, 248258 (by R. T. Rockafellar)

The Euler and Weierstrass conditions for nonsmooth variational
problems, Calculus of Variations & PDE 4 (1996), 5987
(by A. D. Ioffe and R. T. Rockafellar)

Variational conditions and the protodifferentiation of partial subgradient mappings,
Nonlinear Anal. Th. Meth. Appl., 26 (1995), 19511964 (by A. B. Levy and
R. T. Rockafellar)

Sensitivity analysis of solutions to generalized equations,
Trans. Amer. Math. Soc., 345 (1994), 661671(by A. B. Levy and
R. T. Rockafellar).

Basic issues in Lagrangian optimization, in Optimization in
Planning and Operation of Electric Power Systems (K. Frauendorfer, H.
Glavitsch and R. Bacher, eds.), PhysicaVerlag, Heidelberg, 1993, 330
(by R. T. Rockafellar)

Extended linearquadratic programming, SIAG/OPT
ViewsandNews, No. 1 (Fall, 1992), 36 (by R. T. Rockafellar)

Lagrange multipliers and optimality, SIAM Review 35
(1993), 183238 (by R. T. Rockafellar)

Protoderivative formulas for basic subgradient mappings in
mathematical programming, SetValued Analysis 2 (1994),
275290 (by R. A. Poliquin and R. T. Rockafellar)

MATHEMATICS OF DEBT INSTRUMENT TAXATION, Financial Markets,
Institutions and Instruments 3 (1994), 87 pages (by J. C. Dermody and
R. T. Rockafellar)

Subgradients and variational analysis, The Mathematics
Student 62 (1993), 113131 (by R. T. Rockafellar)

Amenable functions in optimization, in Nonsmooth Optimization
Methods and Applications (F. Giannessi, ed.), Gordon and Breach,
Philadelphia, 1992, 338353 (by R.A. Poliquin and R. T. Rockafellar)

Dualization of subgradient conditions for optimality, Nonlin.
Analysis Th. Meth. Appl. 20 (1993), 627646 (by R. T. Rockafellar)

A calculus of epiderivatives applicable to optimization,
Canadian J. Math. 45 (1993), 879896 (by R. A. Poliquin and R. T.
Rockafellar)

Optimal control of unbounded differential inclusions, SIAM J.
Control Opt. 32 (1994), 442470 (by P. D. Loewen and R. T. Rockafellar)

Tax basis and nonlinearity in cash stream valuation, Math.
Finance 5 (1995), 97119 (by J. C. Dermody and R. T. Rockafellar).

Cosmic convergence, in Optimization and Nonlinear Analysis
(A. Ioffe et al., eds.), Pitman Research Notes in Math. Series No.
244, Wiley, 1992, 249272 (by R. T. Rockafellar and R. JB Wets)

A characterization of epiconvergence in terms of convergence of
level sets,
Proc. Amer. Math. Soc. 116 (1992), 753761 (by G. Beer,
R. T. Rockafellar and R. JB Wets).

On a special class of convex functions, J. Optim. Theory
Appl. 70 (1991), 91 (by R. T. Rockafellar).

A dual strategy for the implementation of the aggregation principle
in decision making under uncertainty, J. Applied Stochastic Models and
Data Analysis 8 (1992), 245255 (by R. T. Rockafellar and R. JB Wets)

Primaldual projected gradient algorithms for extended
linearquadratic programming, SIAM J. Optimization 3
(1993), 751783 (by R. T. Rockafellar and C.Y. Zhu)

Asymptotic theory for solutions in generalized Mestimation
and stochastic programming, Math. of Operations Research 18
(1993), 148162 (by A. J. King and R. T. Rockafellar)

Cash stream valuation in the face of transaction costs and taxes,
Math. Finance 1 (1991) 3154
(by J. C. Dermody and R. T. Rockafellar)

Largescale extended linearquadratic programming and multistage
optimization, in Advances in Numerical Partial Differential Equations
and Optimization (S. Gomez, J.P. Hennart, R. Tapia, eds.), SIAM
Publications, 1991, 247261 (by R. T. Rockafellar)

The adjoint arc in nonsmooth optimization,
Trans. Amer. Math. Soc. 325 (1991), 3972 (by P. D. Loewen and
R. T. Rockafellar)

Nonsmooth analysis and parametric optimization, in Methods of
Nonconvex Analysis (A. Cellina, ed.), SpringerVerlag Lecture Notes
in Math. No. 1446 (1990), 137151 (by R. T. Rockafellar)

Sensitivity analysis for nonsmooth generalized equations, Math.
Programming 55 (1992), 193212 (by A. J. King and R. T. Rockafellar)

Hamiltonian trajectories and duality in the optimal control of linear
systems with convex costs, SIAM J. Control Opt. 27 (1989), 10071025

Perturbation of generalized KuhnTucker points in finitedimensional
optimization, in Nonsmooth Optimization and Related Topics, F. H.
Clarke et al. (eds.), Plenum Press, 1989, 393402 (by R. T. Rockafellar)

Computational schemes for largescale problems in extended
linearquadratic programming, Math. Programming 48 (1990), 447474
(by R. T. Rockafellar)

An internal variable theory of elastoplasticity based on the maximum
plastic work inequality, Quart. Appl. Math. 47 (1990),
5983 (by R. A. Eve, B. D. Reddy and R. T. Rockafellar)

Generalized second derivatives of convex functions and saddle functions,
Trans. Amer. Math. Soc. 322 (1990), 5177 (by R. T. Rockafellar)

A finite simplexactiveset algorithm for piecewise quadratic programming,
in Advances in Optimization and Approximation (D.Z. Du and J. Sun,
eds.), Kluwer, 1994, 275292 (by R. T. Rockafellar and J. Sun)

Protodifferentiability of setvalued mappings and its applications
in optimization, in Analyse Non Linéaire, H. Attouch et al.
(eds.), GauthierVillars, Paris, 1989, 449482 (by R. T. Rockafellar)

Scenarios and policy aggregation in optimization under uncertainty,
Math. of Oper. Res. 16 (1991), 119147 (by R. T. Rockafellar and R. JB Wets)

On the essential boundedness of solutions to problems in piecewise
linearquadratic optimal control, in Analyse Mathématique et
Applications, F. Murat and O. Pironneau (eds.), GauthierVillars,
Paris, 1988, 437444 (by R. T. Rockafellar)

Multistage convex programming and discretetime optimal control,
Control and Cybernetics 17 (1988), 225246 (by R. T. Rockafellar).

Generalized linearquadratic problems of deterministic and stochastic
optimal control in discrete time, SIAM J. Control Opt. 28
(1990), 810822 (with R. JB Wets)

Secondorder optimality conditions in nonlinear programming obtained
by way of epiderivatives, Math. of Op. Res. 14 (1989), 462484
(by R. T. Rockafellar).

First and secondorder epidifferentiability in nonlinear programming,
Trans. Amer. Math. Soc. 307 (1988), 75108 (by R. T. Rockafellarf).

A generalized approach to linearquadratic programming,
Proceedings Internat'l Conf. on Numerical Optimization and Appl.
(Xi'an, China, 1986), 5863 (by R. T. Rockafellar).

Linearquadratic programming and optimal control, SIAM J. Control
and Opt. 25 (1987), 781814 (by R. T. Rockafellar).

Lake eutrophication management: the Lake Balaton project, in
Numerical Techniques for Stochastic Optimization Problems, Y.
Ermoliev and R. JB Wets (eds.), SpringerVerlag, 1987, 435448 (by
A. King, R. T. Rockafellar, L. Somlyody and R. JB Wets)

A note about projections in the implementation of stochastic
quasigradient methods, in Numerical Techniques for Stochastic
Optimization Problems, Y. Ermoliev and R. JB Wets (eds.),
SpringerVerlag, 1987, 385392 (by R. T. Rockafellar and R. JB Wets)

Linearquadratic problems with stochastic penalties: the finite
generation algorithm, in Stochastic Optimization , V. I. Arkin, A.
Shiraev and R. JB Wets (eds.), SpringerVerlag Lecture Notes in Control
and Information Sciences No. 81, 1987, 545560 (by R. T. Rockafellar and
R. JB Wets)

Optimization: A case for the development of new mathematical
concepts, J. Computational and Appl. Math. 22 (1988), 243255
(by R. T. Rockafellar).

A Lagrangian finite generation technique for solving linearquadratic
problems in stochastic programming, Math. Programming Studies
28 (1986), 6393 (by R. T. Rockafellar and R. JB Wets).

Lipschitzian properties of multifunctions, Nonlin. Analysis Th.
Meth. Appl. 9 (1985), 867885 (by R. T. Rockafellar).

Lipschitzian stability in optimization: the role of nonsmooth
analysis, in Nondifferentiable Optimization: Motivations and
Applications, V. Demyanov and D. Pallatschke (eds.),
SpringerVerlag Lecture Notes in Economics and Math. Systems No.
255, 1985, 5573 (by R. T. Rockafellar).

Monotropic programming: a generalization of linear programming and
network programming, in Convexity and Duality in Optimization, J.
Ponstein (ed.), SpringerVerlag Lecture Notes in Economics and Math.
Systems, No. 256, 1985, 1036 (by R. T. Rockafellar).

Maximal monotone relations and the second derivatives of nonsmooth
functions, Ann. Inst. H. Poincaré Analyse Non Linéaire 2
(1985), 167184 (by R. T. Rockafellar).

Extensions of subgradient calculus with applications to
optimization, Nonlin. Analysis: Th. Meth. Appl. 9 (1985),
665698 (by R. T. Rockafellar).

NETWORK FLOWS AND MONOTROPIC OPTIMIZATION, WileyInterscience,
1984 (610 pages); republished by Athena Scientific, 1998 (by R. T.
Rockafellar).

Variational systems: an introduction, in Multifunctions and
Integrands, G. Salinetti (ed.), SpringerVerlag Lecture Notes in
Math. No. 1091, 1984, 154 (by R. T. Rockafellar and R. JB Wets).

Automatic step sizes for the descent algorithms in monotropic
programming, in Mathematical Programming, R.W. Cottle et al.
(eds.), Elsevier (NorthHolland), 1984, 337346 (by R. T. Rockafellar).

Directional differentiability of the optimal value function in a
nonlinear programming problem, Math. Programming Studies 21
(1984), 213226 (by R. T. Rockafellar).

Differentiability properties of the minimum value in an optimization
problem depending on parameters, Proceedings of the International
Congress of Mathematicians, Warsaw, 1983, 14191423 (by R. T. Rockafellar).

A dual solution procedure for quadratic stochastic programming
problems with simple recourse, in Numerical Methods, V. Pereyra
and A. Reinoza (eds.), SpringerVerlag Lecture Notes in Math., No.
1005, 1983, 252265 (by R. T. Rockafellar and R. JB Wets).

Generalized subgradients in mathematical programming, in Math.
Programming Bonn 1982  The State of the Art, A. Bachem, M.
Groetschel and B. Korte (eds.), SpringerVerlag, 1983, 368380
(by R. T. Rockafellar).

Marginal values and secondorder conditions for optimality, Math.
Programming 26 (1983), 245286 (by R. T. Rockafellar).

Deterministic and stochastic optimization problems of Bolza type in
discrete time, Stochastics 10 (1983), 273312 (by R. T. Rockafellar
and R. JB Wets).

On the interchange of subdifferentiation and conditional expectation
for convex functionals, Stochastics 7 (1982), 172182 (by R. T.
Rockafellar and R. JB Wets).

Favorable classes of Lipschitz continuous functions in subgradient
optimization, in Progress in Nondifferentiable Optimization, E.
Nurminski (ed.), IIASA Collaborative Proceedings Series, International
Institute of Applied Systems Analysis, Laxenburg, Austria, 1982, 125144
(by R. T. Rockafellar).

Lagrange multipliers and subderivatives of optimal value functions in
nonlinear programming, Math. Programming Study 17 (1982),
2866 (by R. T. Rockafellar).

Generalized subgradients in nonconvex programming, in Math.
Methods in Operations Research, A. Dontchev (ed.), Sofia, 1981,
103110 (by R. T. Rockafellar).

Optimality conditions for convex control problems with nonnegative
states and the possibility of jumps, in Game Theory and Math.
Economics, O. Moeschlin (ed.), NorthHolland, 1981, 339349 (by R. T.
Rockafellar).

Monotropic programming: descent algorithms and duality, in
Nonlinear Programming 4, O.L. Mangasarian (ed.), Academic Press,
1981, 327366 (by R. T. Rockafellar).

Proximal subgradients, marginal values, and augmented Lagrangians in
nonconvex optimization, Math. of Op. Res. 6 (1981),
427437 (by R. T. Rockafellar).

Almost sure existence of Lagrangian price vectors in nonlinear
programming, in Math. Programming and its Applications, C.
Castellani and P. Mazzolini (eds.), Angeli, Milan, 1981, 255262 (by R. T.
Rockafellar).

THE THEORY OF SUBGRADIENTS AND ITS APPLICATIONS TO PROBLEMS OF
OPTIMIZATION: CONVEX AND NONCONVEX FUNCTIONS, HeldermanVerlag,
Berlin, 1981 (107 pages). English version of [82] (by R. T. Rockafellar).

Generalized directional derivatives and subgradients of nonconvex
functions, Canadian J. Math. 32 (1980), 157180 (by R. T. Rockafellar).

Lagrange multipliers and variational inequalities, in Variational
Inequalities and Complementarity Problems, R. W. Cottle, F. Giannessi
and J.L. Lions (eds.), Wiley, 1980, 303322 (by R. T. Rockafellar).

LA THÉORIE DES SOUSGRADIENTS ET SES APPLICATIONS À L'OPTIMISATION:
FONCTIONS CONVEXES ET NON CONVEXES, Collection Chaire Aisenstadt,
Presses de l'Université de Montréal, 1979 (130 pages) (by R. T.
Rockafellar).

The generic nature of optimality conditions in nonlinear
programming, Math. of Oper. Res. 4 (1979), 425430 (by R. T. Rockafellar).

Directionally Lipschitzian functions and subdifferential calculus,
Proc. London Math. Soc. 39 (1979), 331355 (by R. T. Rockafellar).

Convex processes and Hamiltonian dynamical systems, in Convex
Analysis and Math. Economics, J. Kreins (ed.), SpringerVerlag
Lecture Notes in Math. Econ. No. 168, 1979, 122136 (by R. T. Rockafellar).

Clarke's tangent cones and the boundaries of closed sets in
R^{n}, Nonlin. Analysis:
Th. Meth. Appl. 3 (1979), 145154 (by R. T. Rockafellar).

Duality in optimal control, in Mathematical Control Theory,
W. A. Coppel (ed.), SpringerVerlag Lecture Notes in Math. No. 680,
1978, 219257 (by R. T. Rockafellar).

Monotone operators and augmented Lagrangian methods in nonlinear
programming, in Nonlinear Programming 3, O. L. Mangasarian et al.
(eds.), Academic Press, 1978, 125 (by R. T. Rockafellar).

Higher derivatives of conjugate convex functions, Int. J. Applied
Analysis 1 (1977), 4143 (by R. T. Rockafellar).

The optimal recourse problem in discrete time: L^{1}multipliers for inequality constraints,
SIAM J. Control. Opt. 16 (1978) 1636 (R. T. Rockafellar and
R. JB Wets).

Integral functionals, normal integrands and measurable selections, in
Nonlinear Operators and the Calculus of Variations, L. Waelbroeck
(ed.), Lecture notes in Math. No. 543, SpringerVerlag, 1976,
157207 (by R. T. Rockafellar).

Dual problems of Lagrange for arcs of bounded variation, in
Calculus of Variations and Control Theory, D. L. Russell (ed.),
Academic Press, 1976, 155192 (by R. T. Rockafellar).

Augmented Lagrangians and applications of the proximal point
algorithm in convex programming, Math. of Oper. Res. 1
(1976), 97116 (by R. T. Rockafellar).

Measures as Lagrange multipliers in multistage stochastic
programming, J. Math. Analysis Appl. 60 (1977), 301313 (by R. T.
Rockafellar).

A growth property in concaveconvex Hamiltonian systems, J. Econ.
Theory 12 (1976), 191196 (by R. T. Rockafellar).

Nonanticipativity and Lmartingales in stochastic
optimization problems, in Stochastic Systems: Modeling,
Identification, and Optimization, Math. Programming Study
6 (1976), 170187 (by R. T. Rockafellar).

Lagrange multipliers in optimization, SIAMAMS Proceedings,
Vol. 9, R. W. Cottle and C. E. Lemke (eds.), 1976, 145168 (by R. T.
Rockafellar).

Monotone operators and the proximal point algorithm, SIAM J.
Control Opt. 14 (1976), 877898 (by R. T. Rockafellar).

Stochastic convex programming: relatively complete recourse and induced
feasibility,
SIAM J. Control. Opt. 14 (1976) 547589 (by R. T. Rockafellar and
R. JB. Wets).

Semigroups of convex bifunctions generated by Lagrange problems in
the calculus of variations, Math. Scandinavica 36 (1975),
137158 (by R. T. Rockafellar).

Saddle points of Hamiltonian systems in convex Lagrange problems
having a nonzero discount rate, J. Econ. Theory 12 (1976),
71113 (by R. T. Rockafellar).

Stochastic convex programming: KuhnTucker conditions, J. Math.
Econ. 2 (1975), 349370 (by R. T. Rockafellar and R. JB Wets).

On the equivalence of multistage recourse models in stochastic
optimization, in Control Theory, Numerical Methods and Computer
Systems Modelling, Lecture Notes in Econ. and Math. Systems No. 107,
SpringerVerlag, 1974, 314321 (by R. T. Rockafellar).

Solving a nonlinear programming problem by way of a dual problem,
Symposia Mathematica 19 (1976), 135160 (by R. T. Rockafellar).

Lagrange multipliers for an Nstage model in stochastic convex
programming, in Analyse Convexe et Ses Applications, J.P. Aubin
(ed.), SpringerVerlag, 1974, 180187 (by R. T. Rockafellar).

Stochastic convex programming: singular multipliers and extended duality singular multipliers and duality,
Pacific J. Math. 62 (1976), 507522 (by R. T. Rockafellar and
R. J.B. Wets).

Existence theorems for general control problems of Bolza and
Lagrange, Advances in Math. 15 (1975), 315333 (by R. T. Rockafellar).

Stochastic convex programming: basic duality,
Pacific J. Math. 62 (1976), 173195 (by R. T. Rockafellar and
R. J.B. Wets).

Continuous versus measurable recourse in Nstage stochastic
programming, J. Math. Analysis Appl. 48 (1974), 836859 (by R. T.
Rockafellar).

CONJUGATE DUALITY AND OPTIMIZATION, No. 16 in Conference Board
of Math. Sciences Series, SIAM Publications, 1974 (79 pages) (by R. T.
Rockafellar).

Penalty methods and augmented Lagrangians in nonlinear programming,
in Fifth Conference on Optimization Techniques, R. Conti and A.
Ruberti (eds.), SpringerVerlag, 1973, 518525 (by R. T. Rockafellar).

Augmented Lagrange multiplier functions and duality in nonconvex programming,
SIAM J. Control 12 (1974) 268285 (by R. T. Rockafellar).

The multiplier method of Hestenes and Powell applied to convex
programming, J. Opt. Theory Appl. 12 (1973), 555562 (by R. T.
Rockafellar).

A dual approach to solving nonlinear programming problems by
unconstrained optimization, Math. Programming 5 (1973),
354373 (by R. T. Rockafellar).

Convex algebra and duality in dynamic models of production, in
Mathematical Models of Economics, J. Lo´s (ed.), NorthHolland,
1973, 351378 (by R. T. Rockafellar).

Bibliographical supplement to convex analysis, 193 additional items
with comments (22 pages), updating the original bibliography of [25];
published in the Russian edition of the book: Mir, 1973 (by R. T.
Rockafellar).

Dual problems of optimal control, in Techniques of
Optimization, A. V. Balakrishnan (ed.), Academic Press, 1972, 423431 (by
R. T. Rockafellar).

Saddle points of Hamiltonian systems in convex problems of Lagrange,
J. Opt. Theory Appl. 12 (1973), 367390 (by R. T. Rockafellar).

Optimal arcs and the minimum value function in problems of Lagrange,
Trans. Amer. Math. Soc. 180 (1973), 5383 (by R. T. Rockafellar).

State constraints in convex control problems of Bolza,
SIAM J. Control 10 (1972), 691715 (by R. T. Rockafellar).

Convex integral functionals and duality, in Contributions to
Nonlinear Functional Analysis, E. Zaratonello (ed.), Academic Press,
1971, 215236 (by R. T. Rockafellar).

New applications of duality in nonlinear programming, in
Proceedings of the Fourth Conference on Probability Theory (Brasov,
Romania, 1971), Editura Academmi R.S.R., 1973, 7381 (by R. T.
Rockafellar).

Weak compactness of level sets of integral functionals, Troisième
Colloque d'Analyse Fonctionelle (CBRM, Liège, Belgium, 1970), H. G. Garnir
(ed.), 1971, 8598 (by R. T. Rockafellar).

Saddle points and convex analysis, in Differential Games and
Related Topics, H.W. Kuhn and G.P. Szegö (eds.), NorthHolland, 1971,
109128 (by R. T. Rockafellar).

Some convex programs whose duals are linearly constrained,
Nonlinear Programming, J. B. Rosen and O. L. Mangasarian (eds.),
Academic Press, 1970, 293322 (by R. T. Rockafellar).

Existence and duality theorems for convex problems of Bolza,
Trans. Amer. Math. Soc. 159 (1971), 140 (by R. T. Rockafellar).

Ordinary convex programs without a duality gap, J. Opt. Theory
Appl. 7 (1971), 143148 (by R. T. Rockafellar).

Integrals which are convex functionals. II,
Pacific J. Math. 39 (1971), 439–469 (by R. T. Rockafellar).

Generalized Hamiltonian equations for convex problems of Lagrange,
Pacific J. Math. 33 (1970), 411–427 (by R. T. Rockafellar).

Conjugate convex functions in optimal control and the calculus of
variations, J. Math. Analysis Appl. 32 (1970), 174222 (by R. T.
Rockafellar).

Measurable dependence of convex sets and functions on parameters,
J. Math. Analysis Appl. 28 (1969), 425 (by R. T. Rockafellar).

Convex functions, monotone operators and variational inequalities,
in Theory and Applications of Monotone Operators, A. Ghizzetti
(ed.), Tipografia Oderisi Editrice, Gubbio, Italy, 1969, 3465 (by R. T.
Rockafellar).

On the maximal monotonicity of subdifferential mappings,
Pacific J. Math. 33 (1970), 209216 (by R. T. Rockafellar).

On the maximality of sums of nonlinear monotone operators,
Trans. Amer. Math. Soc. 149 (1970), 7588 (by R. T. Rockafellar).

Local boundedness of nonlinear, monotone operators,
Michigan Math. J. 16 (1969), 397407 (by R. T. Rockafellar).

Monotone operators associated with saddlefunctions and minimax
problems, in Nonlinear Functional Analysis, Part 1, F. E. Browder
(ed.), Proceedings of Symposia in Pure Math. 18, Amer. Math.
Soc., 1970, 241250 (by R. T. Rockafellar).

On the virtual convexity of the domain and range of a nonlinear
maximal monotone operator, Math. Annalen 185 (1970), 8190 (by R. T.
Rockafellar).

Convexity properties of nonlinear maximal monotone operators,
Bull. Amer. Math. Soc. 75 (1969), 7477 (by R. T. Rockafellar).

CONVEX ANALYSIS, Vol. 28 of Princeton Math. Series, Princeton
Univ. Press, 1970 (470 pages) (by R. T. Rockafellar). Also available
from 1997 in paperback from the same publisher, in the series Princeton
Landmarks in Mathematics and Physics.

Convex functions and duality in optimization problems and dynamics,
in Mathematical Systems Theory and Economics I, H. W. Kuhn and G.
P. Szegö (eds.), SpringerVerlag, 1969, 117141 (by R. T. Rockafellar).

Conjugate convex functions in nonlinear programming, in
Proceedings of the Sixth International Symposium on Math.
Programming, H. W. Kuhn and A. W. Tucker (eds.), Dept. of Math.,
Princeton University, 1970, 418485 (by R. T. Rockafellar).

Duality in nonlinear programming, in Mathematics of the Decision
Sciences, Part 1, G. B. Dantzig and A. F. Veinott (eds.), Lectures
n Applied Math., Vol. II, Amer. Math. Soc., 1968, 401422 (by R. T.
Rockafellar).

Gradients of convex functions,
Trans. Amer. Math. Soc. 139 (1969), 443467 (by E. Asplund and R. T.
Rockafellar).

The elementary vectors of a subspace of R^{n}, in Combinatorial Mathematics and its
Applications, R. C. Bose and T. A. Dowling (eds.), Univ. of North
Carolina Press, 1969, 104127 (by R. T. Rockafellar).

A model of cell cleavage,
Biophys. J. 7 (1967), 659673 (by J. Prothero and R. T. Rockafellar).

Convex functions on convex polytopes,
Proc. Amer. Math. Soc. 19 (1968), 867873 (by D. Gale, V. L. Klee and
R. T. Rockafellar).

Integrals which are convex functionals,,
Pacific J. Math. 24, no. 3 (1968), 525539 (by R. T. Rockafellar).

Convex programming and systems of elementary monotonic relations,
J. Math. Analysis Appl. 19 (1967), 167187 (by R. T. Rockafellar).

A monotone convex analog of linear algebra, in Proc. Colloquium
on Convexity, Copenhagen, 1965, W. Fenchel (ed.), Matematisk Institut,
Copenhagen, 1967, 261276 (by R. T. Rockafellar).

Conjugates and Legendre transforms of convex functions, Canad. J.
Math. 19 (1967), 200205 (by R. T. Rockafellar).

A general correspondence between dual minimax problems and convex programs,
Pacific J. Math. 25 (1968), 597611 (by R. T. Rockafellar).

Duality and stability in extremum problems involving convex functions,
Pacific J. Math. 21 (1967), 167–187 (by R. T. Rockafellar).

MONOTONE PROCESSES OF CONVEX AND CONCAVE TYPE, Memoir 77, Amer.
Math. Soc., 1967 (79 pages) (by R. T. Rockafellar).

Characterization of the subdifferentials of convex functions,
Pacific J. Math. 17 (1966), 497–510 (by R. T. Rockafellar).

Minimax theorems and conjugate saddlefunctions, Math.
Scandinavica 14 (1964), 151173 (by R. T. Rockafellar).

Extension of Fenchel's duality theorem for convex functions,
Duke Math. J. 33 (1966), 8189 (by R. T. Rockafellar).

On the subdifferentiability of convex functions,
Proc. Amer. Math. Soc. 16 (1965), 605611 (by A. Brøndsted and R. T.
Rockafellar).

Level sets and continuity of conjugate convex functions,
Trans. Amer. Math. Soc. 123 (1966), 4663 (by R. T. Rockafellar).

Helly’s theorem and minima of convex functions,
Duke Math. J. 32 (1965), 381–39 (by R. T. Rockafellar).

A necessary condition for the existence of best approximations,
J. Math. Mech. 13 (1964), 10371038 (by B. Kripke and R. T. Rockafellar).

A combinatorial algorithm for linear programs in the general mixed form,
SIAM J. 12 (1964), 215225 (by R. T. Rockafellar).

Duality theorems for convex functions, Bull. Amer. Math. Soc.
70 (1964), 189192 (by R. T. Rockafellar).

CONVEX FUNCTIONS AND DUAL EXTREMUM PROBLEMS, doctoral
dissertation, Dept. of Mathematics, Harvard University, 1963 (165 pages)
(by R. T. Rockafellar).