Contact information:
Mathematics Department, University of Washington
Seattle, WA 98195
ddrusv_at_uw.edu

## West Coast Optimizaion Meeting (WCOM) 2018

I am an Assistant Professor at the Mathematics Department of University of Washington. My interests are in nonsmooth optimization, variational analysis, and the connections of these disciplines to semi-algebraic geometry. See my Curriculum Vitae for more details.

## New NSF TRIPODS institute

This new Institute in Transdisciplinary Research in Principles of Data Science (TRIPODS) is led by Zaid Harchaoui (Statistics), Maryam Fazel (CSE), Yin Tat Lee (CSE), Sham Kakade (CSE), and myself. Click on the link above to see our activities and more information about the institute.

## Preprints/Articles in review

1. Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functions (with D. Davis)
Manuscript, 12 pages, 2018.
Supplementary technical note: Complexity of finding near-stationary points of convex functions stochastically
2. The nonsmooth landscape of phase retrieval (with D. Davis and C. Paquette)
Manuscript, 42 pages, 2017.
3. Catalyst acceleration for gradient-based non-convex optimization (w/ C. Paquette, H. Lin, J. Mairal, Z. Harchaoui)
Preprint, 30 pages, 2017.
4. Foundations of gauge and perspective duality (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and K. MacPhee)
Manuscript, 28 pages, 2017.
5. Efficiency of minimizing compositions of convex functions and smooth maps (with C. Paquette)
Manuscript, 38 pages, 2016.
6. Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria (with A.D. Ioffe and A.S. Lewis)
Manuscript, 23 pages, 2016.
7. Level-set methods for convex optimization (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and S. Roy)
Manuscript, 38 pages, 2016.

## Expository writing

1. The proximal point method revisited
Submitted to SIAG/OPT Views and News, 2017.
2. The many faces of degeneracy in conic optimization (with H. Wolkowicz)
Foundations and Trends in Optimization, Vol. 3, No. 2, pp 77-170, 2017.
3. Semi-algebraic geometry
Chapter 8.3 in the book "Variational Analysis of Regular Mappings: Theory and Applications" by Alexander Ioffe, Springer Monographs in Mathematics, 2017.

## Publications (accepted or appeared)

1. Error bounds, quadratic growth, and linear convergence of proximal methods (with A.S. Lewis)
To appear in Math. Oper. Res. 2017.
2. Noisy Euclidean distance realization: robust facial reduction and the Pareto frontier
(with N. Krislock, Y.-L. Voronin, and H. Wolkowicz), Matlab code
SIAM J. Optim. 27(4):2301-2331, 2017.
3. Efficient quadratic penalization through the partial minimization technique (with A.Y. Aravkin and T. van Leeuwen)
To appear in IEEE Trans. Automat. Contr., 2017.
4. An optimal first order method based on optimal quadratic averaging (with M. Fazel and S. Roy), Matlab code
To appear in SIAM J. Optim., 2016.
5. Sweeping by a tame process (with A. Daniilidis)
To appear in Ann. Inst. Fourier (Grenoble), 2016.
6. Variational analysis of spectral functions simplified (with C. Paquette)
J. Convex Anal. 25(1), 2018.
7. The Euclidean distance degree of orthogonally invariant matrix varieties (with H.-L. Lee, G. Ottaviani, R.R. Thomas)
To appear in Israel J. Math., 2017.
8. A note on alternating projections for ill-posed semidefinite feasibility problems (with G. Li and H. Wolkowicz)
Math. Program. 162(1-2):537-548, 2017.
9. Generic minimizing behavior in semi-algebraic optimization (with A.D. Ioffe, A.S. Lewis)
SIAM J. Optim. 26(1):513-534, 2016.
10. Transversality and alternating projections for nonconvex sets (with A.D. Ioffe, A.S. Lewis)
Found. Comput. Math. 15(6):1637-1651, 2015.
11. Counting real critical points of the distance to orthogonally invariant matrix sets (with H.-L. Lee, R.R. Thomas)
SIAM J. Matrix Anal. Applic. 36(3):1360-1380, 2015.
12. Quadratic growth and critical point stability of semi-algebraic functions (with A.D. Ioffe)
Math. Program. Ser. A., 153(2):635-653, 2015.
13. Projection methods for quantum channel construction (with C.-K. Li, D.C. Pelejo, Y.-L. Voronin, H. Wolkowicz)
Quantum Inf. Process., 14(8): 3075-3095, 2015.
14. Extreme point inequalities and geometry of the rank sparsity ball (with S.A. Vavasis, H. Wolkowicz)
Math. Program. Ser. A, 152(1-2): 521-544, 2015.
15. Coordinate shadows of semi-definite and Euclidean distance matrices (with G. Pataki, H. Wolkowicz)
SIAM J. Optim., 25(2): 1160-1178, 2015.
16. Clarke subgradients for directionally Lipschitzian stratifiable functions (with A.D. Ioffe, A.S. Lewis)
Math. Oper. Res. 40(2): 328-349, 2015.
17. Curves of descent (with A.D. Ioffe, A.S. Lewis)
SIAM J. Control and Optim., 53(1): 114-138, 2015.
18. Approximating functions on stratified sets (with M. Larsson)
Trans. Amer. Math. Soc. 367, 725-749, 2015.
19. Orbits of geometric descent (with A. Daniilidis, A.S. Lewis)
Canad. Math. Bull., 58(1): 44-50, 2015.
20. Orthogonal invariance and identifiability (with A. Daniilidis, A.S. Lewis)
SIAM J. Matrix Anal. Applic., 35(2): 580-598, 2014.
21. Optimality, identifiability, and sensitivity (with A.S. Lewis)
Math. Program. Ser. A, (147)1: 467-498, 2014. Long version
22. Second-order growth, tilt stability, and metric regularity of the subdifferential (w/ B.S. Mordukhovich, T.T.A. Nghia)
J. Convex Anal., 21(4): 1165-1192, 2014.
23. Semi-algebraic functions have small subdifferentials (with A.S. Lewis)
Math. Program. Ser. B., 140(1): 5-29, 2013.
24. Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential (with A.S. Lewis)
SIAM J. Optim., 23(1): 256-267, 2013.
25. The dimension of semi-algebraic subdifferential graphs (with A.S. Lewis, A.D. Ioffe)
Nonlinear Analysis, 75(3):1231-1245, 2012.
26. Generic nondegeneracy in convex optimization (with A.S. Lewis)
Proc. Amer. Math. Soc. 139, 2519-2527, 2011.

## Invited Research Talks

• Slope and geometry in variational mathematics, CNA Seminar, Carnegie Mellon, Pittsburgh, PA, Jan. 2018.
• Algorithms for minimizing compositions of convex functions and smooth maps, CS Theory Seminar, University of Washington, Seattle, WA, Dec. 2017. Slides
• Structure, complexity, and conditioning in nonsmooth optimization, Mathematics colloquium, UCSD, San Diego, CA, Nov. 2017.
• Composite nonlinear models at scale, ORIE colloquium, Cornell, Ithaca, NY, Nov. 2017. Slides
• Efficiency of minimizing compositions of convex functions and smooth maps, Foundations of Computational Mathematics (FoCM 2017), Barcelona, Spain, July 2017. Slides
• Taylor-like models in nonsmooth optimization, SIAM Conf. on Optimization, Vancouver, Canada, May 2017. Slides
• Efficiency of inner-outer algorithms at scale, Optimization and Statistical Learning, Les Houches, France, April 2017. Slides
• Expanding the reach of optimal methods (conference organizer), West Coast Optimization Meeting (WCOM 2016), University of Washington, USA, May 2016. Slides
• Geometry of orthogonally invariant matrix varieties, Algebra & Discrete Mathematics Seminar, UC Davis, USA, Apr. 2016. Slides
• Tame variational analysis, Variational analysis and applications, Erice, Italy, Aug. 2015.
• Slope and variational geometry in optimization, International Symposium on Mathematical Programming (ISMP 2015), A.W. Tucker prize session, Pittsburgh, USA, Jul. 2015. Slides
The many faces of degeneracy in conic optimization, International Symposium on Mathematical Programming (ISMP 2015), Pittsburgh, USA, Jul. 2015. Slides
• Tame variational analysis, International conference on Variational Analysis, Optimization, and Quantitative Finance (Terry Fest), Université de Limoges, France, May. 2015. Slides
• Feasibility problems: from alternating projections to matrix completions, Joint meeting of the Israel Math. Union - American Math. Soc., Tel Aviv University, Israel, Jun. 2014. Slides
• Feasibility problems: from alternating projections to matrix completions, SIAM Conference on Optimization, San Diego, CA, May. 2014.
• Feasibility problems: from alternating projections to matrix completions, Tutte Seminar, University of Waterloo, Waterloo, Canada, Mar. 2014. Slides
• Slope and geometry in variational mathematics, Optimization and Equilibrium Seminar, DIM-CMM Universidad de Chile, Santiago, Chile, Nov. 2013.
• Slope and geometry in variational mathematics, Midwest Optimization Meeting, University of Western Ontario, ON, Canada, Oct. 2013.
• Slope and geometry in variational mathematics, West Coast Optimization Meeting (WCOM 2013), University of Victoria, BC, Canada, Oct. 2013. Slides
• Optimization and intrinsic geometry (session chair), International Conference on Continuous Optimization (ICCOPT 2013), Caparica, Portugal, Jul. 2013. Slides
• Optimization and intrinsic geometry, ISE seminar, Lehigh University, Bethlehem, Pennsylvania, Feb. 2013. Slides
• Slope and geometry in variational mathematics, South Pacific Optimization Meeting (SPOM 2013), The University of Newcastle, Newcastle, Australia, Feb. 2013. Slides
• Slope and geometry in variational mathematics, UW-PIMS Mathematics Colloquium, University of Washington, Seattle, Washington, USA, Jan. 2013. Slides
• Active sets, steepest descent, and smooth approximations of functions, Combinatorics and Optimization Seminar, University of Waterloo, Waterloo, Ontario, Canada, Jan. 2013. Slides
• Active sets, steepest descent, and smooth approximations of functions, Nonlinear Analysis and Optimization Seminar, Technion - Israel Institute of Tech., Haifa, Israel, Nov. 2012. Slides
• Active sets, steepest descent, and smooth approximations of functions, UW Optimization seminar, University of Washington, Seattle, Washington, USA, Oct. 2012. Slides
• Identifiability and the foundations of sensitivity analysis, International Symposium on Mathematical Programming, Berlin Institute of Technology, Berlin, Germany, Aug. 2012. Slides
• Variational analysis and smooth substructure, Constructive Nonsmooth Analysis and Related Topics, Euler International Mathematical Institute, St. Petersburg, Russia, June 2012. Slides
• Variational analysis and smooth substructure, Variational Analysis and Applications, Erice, Sicily, May 2012. Slides
• Variational analysis and smooth substructure, Seminar on Nonlinear Analysis and Optimization, Technion - Israel Institute of Technology, Haifa, Israel, Jan. 2012. Slides