Publications By Year

2021

• Convergence of the Gradient Sampling Algorithm on Directionally Lipschitz Functions,
  with Q.Lin. Set-Valued and Variational Analysis, 29 (2021) 949--996. (DOI 10.1007/s11228-021-00610-3)
• A study of convex convex-composite functions via infimal convolution with applications
  with Tim Hoheisel and Quang V. Nguyen. Published online in Mathematics of Operations Research (2021). https://doi.org/10.1287/moor.2020.1099.
• Algorithms for Block Tridiagonal Systems: Foundations and New Results for Generalized Kalman Smoothing,
  with A.Aravkin, B.Bell, and G.Pillonetto. To appear in 19th IFAC Symposium on System Identification (SYSID 2021).
• On the Global Minimizers of Real Robust Phase Retrieval with Sparse Noise
  with Aleksandr Aravkin and Daiwei He. IEEE Transactions on Information Theory, 67(2021)pp. 1886-1896. DOI: 10.1109/TIT.2020.3040959

• Generalized Kalman Smoothing: Modeling and Algorithms.
  with Aleksandr Aravkin, Lennart Ljung, Aurelie Lozano, and Gianluigi Pillonetto. Automatica 86(2017): 63 - 86.
• Epi-convergence Properties of Smoothing by Infimal Convolution.
  with T.Hoheisel. Set-Valued and Variational Analysis 25(2017): 1 - 23.

2015

• Matrix support functionals for inverse problems, regularization, and learning.
  with T.Hoheisel, SIAM J. Optim. 25(2015): 1135 - 1159.
• Iteratively Reweighted Linear Least Squares for Exact Penalty Subproblems on Product Sets.
  with F.Curtis, H.Wang and J.Wang, SIAM J. Optim.. 25(2015): 261 - 294.
• The connection between Bayesian estimation of a Gaussian random field and RKHS.
  with A.Y. Aravkin, B.M. Bell and G. Pillonetto, IEEE Transactions on Neural Networks and Learning Systems. 26(2015): 1518 - 1524.

2014

• Smoothing dynamical systems with state-dependent covariance matrices.
  with A.Y.Aravkin. IEEE 53rd Annual Conference on Decision and Control (CDC), 2014, pages 3382 - 3387.
• Robust and Trend-following Student's t Kalman Smoothers.
  with A.Y. Aravkin and G. Pillonetto, SIAM J. Control Optim. 52(2014): 2891-2916.
• Convex vs. nonconvex approaches for sparse estimation: GLasso, multiple kernel learning, and HGLasso,
  with A.Y. Aravkin, A. Chiuso, and G. Pillonetto, Journal of Machine Learning Research, 15(2014) 217-252.
• A sequential quadratic programming optimization algorithm with rapid infeasibility detection.
  with F. Curtis and H. Wang, SIAM J. Optimization, 24(2014):839--872.
• Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation.
  with A.Y. Aravkin and G. Pillonetto, In Compressed Sensing & Sparse Filtering, eds., A. Carmi, L. Mihaylova, and S. Godsill. Springer. pp. 237-281, 2014.

2013

• Linear system identification using stable spline kernels and PLQ penalties.
  with A.Y. Aravkin and G. Pillonetto, Proceedings of the 52nd IEEE Conf. Decision and Control (CDC), December 2013, pp. 5168-5173.
• Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory.
  with A.Y. Aravkin and G. Pillonetto, Journal of Machine Learning Research, 14(2013) 2689-2728.
• Epi-convergent smoothing with applications to convex composite functions.
  with T. Hoheisel, Siam J. Optimization, 23(2013) 1457 - 1479.
• Variational Properties of Value Functions.
  with A.Y. Aravkin and M.P. Friedlander, SIAM Journal of Optimization, 23(2013) 1689 - 1717.
• Gradient consistency for integral-convolution smoothing functions.
  with T. Hoheisel and Christian Kanzow, Set-Valued and Variational Analysis, 21(2013) 359 -- 376.

2012

• On the MSE properties of empirical Bayes methods for sparse estimation,
  with A.Y.Aravkin, A.Chiuso, and G.Pillonetto, IFAC Systems Identification, Volume 16, Part 1, Pages 965-970, 2012.
• Robust and trend following Kalman smoothers using Student's t,
  with A.Y.Aravkin and G.Pillonetto, IFAC Systems Identification, Volume 16, Part 1, Pages 1215-1220, 2012.
• A statistical and computational theory for robust and sparse Kalman smoothing,
  with A.Y.Aravkin and G.Pillonetto, IFAC Systems Identification, Volume 16, Part 1, Pages 894-899, 2012.
• On the estimation of hyper parameters for empirical Bayes estimators: maximum marginal likelihood vs. minimum MSE,
  with A.Y.Aravkin, A.Chiuso, and G.Pillonetto, IFAC Systems Identification, Volume 16, Part 1, Pages 125-130, 2012.
• On the subdifferential regularity of max root functions for polynomials,
  with Julia Eaton, Journal of Nonlinear Analysis Series A: Theory, Methods & Applications, 75(2012) 1168--1187.
• Nonsmooth regression and state estimation using piecewise quadratic log-concave densities.
  with A.Y. Aravkin and G.Pillonetto. Proceedings of the 51st IEEE Conf. Decision and Control (CDC), 2012, pp. 4101-4106.

2011

• Convex vs. non-convex approaches to sparse estimation: LASSO, multiple kernel learning, and hyperparameter LASSO,
  with A.Y.Aravkin, A.Chiuso, and G.Pillonetto, Proceedings of the IEEE Conference on Decision and Control (CDC), 2011, pp. 156--161.
• Learning using state space kernel machines,
  with A.Y.Aravkin, B.Bell, and G.Pillonetto, IFAC World Congress, Volume 18, Part 1, pages 2296-2302, 2011.
• A nonlinear sparsity promoting formulation and algorithm for full-waveform inversion,
  with A.Y.Aravkin, T. van Leeuwen, and F.J.Herrmann, 73rd EAGE Expanded Abstracts, 2011.
• An l_1-Laplace Robust Kalman Smoother,
  with Aleksandr Aravkin, Bradley Bell and Gianluigi Pillonetto, IEEE Transactions on Automatic Control, 56(2011) 2898--2911,

2009

• An Inequality Constrained Kalman-Bucy Smoother by Interior Point Likelihood Maximization,
  with Bradley Bell and Gianluigi Pillonetto, Automatica, 45(2009) 25-33.
• Weak sharp minima revisited, part III: error bounds for differentiable convex inclusions,
  with Sien Deng, Mathematical Programming, 116(2009) 37-56.

2008

• Algorithmic Differentiation of implicit functions and Optimal Values,
  with Bradley Bell, in Advances in Automatic Differentiation, Eds. C. Bischof, H. Bucker, P. Hovland, U. Naumann, and J. Utke, Springer, 2008, pp. 67-77.
• The Speed of Shor's R-Algorithm,
  with Adrian S. Lewis and Michael L. Overton, IMA Journal of Numerical Analysis, 28(2008) 711-720.

2007

• Spectral conditioning and pseudospectral growth,
  with Adrian S. Lewis, and Michael L. Overton. Numerische Mathematik, 107(2007) 27-37.
• Convexity and Lipschitz behavior for small pseudospectra,
  with Adrian S. Lewis and Michael L. Overton, SIAM J. Matrix Analysis, 29(2007) 586-595.

2006

• HIFOO - A MATLAB package for fixed-order controller design and H-infinity optimization,
  with Didier Henrion, Adrian S. Lewis, and Michael L. Overton, in the proceedings of the International Federation of Automatic Control Conference on Robust Control Design, Toulouse, July 2006.
• Stabilization via nonsmooth, nonconvex optimization,
  with Didier Henrion, Adrian S. Lewis, and Michael L. Overton, IEEE Transactions on Automatic Control, 51(2006) 1760-1769.
• Characterizations of the Polynomial Numerical Hull of Degree k,
  with Anne Greenbaum, Lin. Alg. Appl., 419(2006) 37-47.

2005

• Weak sharp minima revisited, Part II: Applications to Linear Regularity and Error Bounds,
  with Sien Deng, Mathematical Programming, 104(2005) 236-261.
• Variational Analysis of Functions of the Roots of Polynomials,
  with Adrian Lewis and Michael Overton, Mathematical Programming, 104(2005) 263-292.
• A robust gradient sampling algorithm for nonsmooth, nonconvex optimization,
  with Michael Overton and Adrian Lewis, SIAM J. Optimization, 15(2005) 751-779.
• A new proximal point iteration that converges weakly but not in norm,
  with H. H. Bauschke, F. R. Deutsch, H. S. Hundal, and J. D. Vanderwerff, Proc. Amer. Math. Soc., 133(2005), 1829-1835.

2004

• Pseudospectral components and distance to controllability,
  with Michael Overton and Adrian Lewis, SIAM J. Matrix Anal. Appl., 26(2004) 350-361.
• Variational analysis of the abscissa mapping for polynomials via the Gauss-Lukas theorem,
  with Adrian Lewis and Michael Overton, J. Global Optimization, 28(2004), 259--268.
• Differentiability of cone-monotone functions on separable Banach space,
  with Jonathan Borwein and Adrian Lewis, Proc. of the American Math. Soc., 132(2004), 1067--1076.

2003

• A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers,
  with Michael Overton and Adrian Lewis, Proceedings of the International Federation of Automatic Control, Milan, June, 2003, Conference on Robust Control Design.
• Robust stability and a criss-cross algorithm for pseudospectra,
  with Adrian Lewis and Michael Overton, IMA J Num Anal, 23(2003), 359--375.
• Variational analysis applied to the problem of optical phase retrieval,
  with Russell Luke, SIAM J. Control and Optimization, 42(2003), 576--575.
• Optimization and Pseudospectra, with applications to robust stability,
  with Adrian Lewis and Michael Overton, SIAM Journal on Matrix Analysis and Applications, 25(2003), 80--104.

2002

• Weak sharp minima revisited, Part I: basic theory,
  Control & Cybernetics, 31(2002), 439--469.
• Optical wavefront reconstruction: theory and numerical methods,
  with Russell Luke, SIAM Review, 44(2002), 169--224.
• Two numerical methods for optimizing matrix stability,
  with Adrian Lewis and Michael Overton, Linear Algebra and its Applications, 351-352(2002), 117--145.
• Approximating subdifferentials by random sampling of gradients,
  with Adrian Lewis and Michael Overton, Mathematics of Operations Research, 27(2002), 567--584.
• The complexity of a non-interior path following method for the linear complementarity problem,
  with Song Xu, J. Optimization Theory and Applications, 112(2002), 53--76.

2001

• Optimal stability and eigenvalue multiplicity,
  with Adrian Lewis and Michael Overton, Foundations of Computational Mathematics, 1(2001), 205--225.
• Variational analysis of non--Lipschitz spectral functions,
  with Michael Overton, Math. Programming, 90(2001), 317--351.
• Optimizing matrix stability,
  with Adrian Lewis and Michael Overton, Proc. of the American Math. Soc., 129(2001), 1635--1642.

2000

• Variational analysis of the abscissa mapping for polynomials,
  with Michael Overton, SIAM Journal on Control and Optimization, 39(2000), 1651--1676.
• Fast algorithms for phase diversity and phase retrieval,
  with Russell Luke and Richard Lyon, Proceedings for the Workshop on Computational Optics and Imaging for Space Applications: May 2000, Editor: Richard Lyon, NASA/Goddard Space Fight Center.
• A non--interior predictor--corrector path following algorithm for the monotone linear complementarity problem,
  with Song Xu, Mathematical Programming, 87(2000), 113--130.
• On the super--linear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating,
  with M. Qian, Mathematical Programming, 88(2000), 157--181.

1999

• The global linear convergence of a non--interior path--following algorithm for linear complementarity problems,
  with S. Xu, Mathematics of Operations Research, 23(1999), 719--734.
• A polynomial time interior--point path--following algorithm for LCP based on Chen--Harker--Kanzow smoothing techniques,
  with S. Xu, Mathematical Programming, 86 (1999), 91--103.
• The variable metric proximal point algorithm for monotone operators,
  with M. Qian, SIAM J. Control and Optimization, 37 (1999), 353--375.

1998

• On the local super-linear convergence of a matrix secant implementation of the variable metric proximal point algorithm for monotone operators,
  with M. Qian, Reformulation-- Nonsmooth, Piecewise Smooth, Semi--smooth, and Smoothing Methods, Editors: Liqun Qi and Masao Fukushima, Kluwer Academic Publishers, 1998, pp. 317--334.
• A non--interior predictor--corrector path following method for LCP,
  with S. Xu, Reformulation-- Nonsmooth, Piecewise Smooth, Semi--smooth, and Smoothing Methods, Editors: Liqun Qi and Masao Fukushima, Kluwer Academic Publishers, 1998, pp. 45--64.

1997

• On the Lidskii--Vishik--Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure,
  with J. Moro and M. L. Overton, SIAM J. Matrix Anal. Appl., 18 (1997), 793--817.

1996

• A relative weighting method for estimating parameters and variances in multiple data sets,
  with B. Bell and A. Schumitzky, Computational Statistics and Data Analysis, 22 (1996), 119--135.
• A Gauss--Newton method for convex composite optimization,
  with M. C. Ferris, Mathematical Programming, 71 (1996), 179--194.
• A unified analysis of Hoffman's bound via Fenchel duality,
  with P. Tseng, SIAM J. Optimization, 6 (1996), 265--282.

1994

• Differential properties of the spectral abscissa and the spectral radius for analytic matrix-valued mappings,
  with M. L. Overton, Journal of Nonlinear Analysis, Theory, Methods, and Applications, 23(1994), 467--488.
• Exposing constraints,
  SIAM J. Optimization, 4(1994), 573--595.

1993

• Translational cuts for minimization,
  with A. A. Goldstein, P. Tseng, and Yinyu Ye, Complexity in Numerical Optimization, Ed. P. Pardalos, (1993) pp. 57--72.
• Weak sharp minima in Mathematical programming,
  with M. C. Ferris, SIAM J. Control and Optimization, 31(1993), 1340--1359.

1992

• On the subdifferentiability of functions of a matrix spectrum, II: Subdifferential formulas,
  with M. L. Overton, Nonsmooth Optimization: Methods and Applications, Ed. F. Giannessi, (1992) pp. 19--29.
• On the subdifferentiability of functions of a matrix spectrum, I: Mathematical foundations,
  with M. L. Overton, Nonsmooth Optimization: Methods and Applications, Ed. F. Giannessi, (1992) pp. 11--18.
• Stable perturbations of nonsymmetric matrices,
  with M. L. Overton, Linear Algebra and Its Applications, 171(1992), 249--273.
• On the Clarke subdifferential of the distance function to a closed set,
  with M. C. Ferris and M. Qian, J. Math. Analysis and Applications, 166 (1992), 199--213.
• A robust trust region method for constrained optimization,
  SIAM J. Optimization, 2(1992), 325--347.
• Optimality conditions for non-finite valued convex composite functions,
  with R. Poliquin, Mathematical Programming, 57 (1992), 103--120.

1991

• Weak directionally closed generalized subdifferentials,
  with L.Qi, J. Math. Analysis and Applications, 159(1991), 485--499.
• An exact penalization viewpoint of constrained optimization,
  SIAM J. Control and Optimization, 29 (1991), 968--998.
• Calmness and exact penalization,
  SIAM J. Control and Optimization, 29 (1991), 493--497.

1990

• Characterization of solution sets to convex programs,
  with M.C.Ferris, Operations Research Letters, 10 (1990), 57--60.
• On the identification of active constraints II: the nonconvex case,
  SIAM J. Numer. Anal., 27 (1990), 1081-1102.
• Convergence properties of trust region methods for linear and convex constraints,
  with J.J.More and G.Toraldo, Mathematical Programming, 47 (1990), 305-336.

1989

• A sequential quadratic programming method for potentially infeasible mathematical programs,
  J. Math. Analysis and Applications, 139 (1989), 319--351.
• A robust sequential quadratic programming method,
  with S.-P.Han, Mathematical Programming, 43 (1989), 277--303.

1988

• On the identification of active constraints,
  with J.J.More, SIAM J. Numer. Anal., 25 (1988), 1197--1211.

1987

• Second order necessary and sufficient conditions for convex composite NDO,
  Mathematical Programming, 38 (1987), 287--302.

1986

• A Gauss-Newton approach to solving generalized inequalities,
  with S.-P.~Han, Mathematics of Operations Research, 11 (1986), 632--643.

1985

• > Descent methods for composite nondifferentiable optimization problems,
  Mathematical Programming, 33 (1985), 260--279.