About me:
I am an Associate Professor at the Mathematics Department of University of Washington. I work in continuous optimization, with an emphasis on largescale problems that arise in data scientific applications. I use tools from convex and nonlinear optimization, variational analysis, semialgebraic geometry, and highdimensional probability and statistics. See my Curriculum Vitae for more details.
NSF TRIPODS institute:
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. This summer, the institute is organizing the ADSI Workshop and Summer School. Please click on the links below for details.Workshop, Aug 1921: Foundations of Learning and Control Workshop
Summer School, Aug 1317: Foundations of Data Science School
Current courses
Preprints/Articles in review

From low probability to high confidence in stochastic convex optimization (with D. Davis, L. Xiao, J. Zhang)
Manuscript, 37 pages, 2019. 
Stochastic algorithms with geometric step decay converge linearly on sharp functions
(with D. Davis, V. Charisopoulos)
Manuscript, 42 pages, 2019. Code 
Lowrank matrix recovery with composite optimization: good conditioning and rapid convergence
(with V. Charisopoulos, Y. Chen, D. Davis, M. Diaz, L. Ding)
Manuscript, 80 pages, 2019. Code 
Composite optimization for robust blind deconvolution (with V. Charisopoulos, D. Davis, M. Diaz)
Manuscript, 60 pages, 2018. Code 
Graphical convergence of subgradients in
nonconvex optimization and learning (with D. Davis)
Manuscript, 35 pages, 2018. 
Stochastic modelbased minimization under highorder growth (with D. Davis and K.J. MacPhee)
Manuscript, 30 pages, 2018.
Expository writing

The proximal point method revisited
SIAG/OPT Views and News, Vol. 26, No. 1, 2018. 
The many faces of degeneracy in conic optimization (with H. Wolkowicz)
Foundations and Trends in Optimization, Vol. 3, No. 2, pp 77170, 2017. 
Semialgebraic 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)

Levelset methods for convex optimization (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and S. Roy)
To appear in Math. Program. Ser. B, 2018. 
Inexact alternating projections on nonconvex sets (with A.S. Lewis)
To appear in Vietnam J. Math., Special issue in honor of Alex Ioffe, 2018. 
Stochastic subgradient method converges
on tame functions (with D. Davis, S. Kakade, and J.D. Lee)
To appear in Found. Comput. Math., 2018. 
Stochastic modelbased minimization of weakly convex functions (with D. Davis)
To appear in SIAM J. Optim., 2018.
This is the combination of the two arXiv preprints arXiv:1802.02988 and arXiv:1803.06523
Supplementary technical note: Complexity of finding nearstationary points of convex functions stochastically 
The nonsmooth landscape of phase retrieval (with D. Davis and C. Paquette)
To appear in IMA J. Numer. Anal., 2018. 
Efficiency of minimizing compositions of convex functions and smooth maps (with C. Paquette)
To appear in Math. Program., 2018. 
Subgradient methods for sharp weakly convex functions (with D. Davis, K.J. MacPhee, and C. Paquette)
J. Optim. Theory App. 179(3):962982, 2018. 
Foundations of gauge and perspective duality (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and K. MacPhee)
SIAM J. Optim. 28(3):24062434, 2018. 
Error bounds, quadratic growth, and linear convergence of proximal methods (with A.S. Lewis)
Math. Oper. Res. 43(3):919948, 2018. 
Efficient quadratic penalization through the partial minimization technique (with A.Y. Aravkin and T. van Leeuwen)
IEEE Trans. Automat. Contr. 63(7):21312138, 2018. 
An optimal first order method based on optimal quadratic averaging (with M. Fazel and S. Roy), Matlab code
SIAM J. Optim. 28(1):251271, 2018. 
Variational analysis of spectral functions simplified (with C. Paquette)
J. Convex Anal. 25(1):119134, 2018. 
The Euclidean distance degree of orthogonally invariant matrix varieties (with H.L. Lee, G. Ottaviani, R.R. Thomas)
Israel J. Math. 221(1):291316 2017. 
Sweeping by a tame process (with A. Daniilidis)
Ann. Inst. Fourier (Grenoble) 67(5):22012223, 2017. 
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):23012331, 2017. 
A note on alternating projections for illposed semidefinite feasibility problems (with G. Li and H. Wolkowicz)
Math. Program. 162(12):537548, 2017. 
Nonsmooth optimization using Taylorlike models: error bounds, convergence, and termination criteria
(with A.D. Ioffe and A.S. Lewis)
To appear in Math. Program. Ser. A, 2016. 
Generic minimizing behavior in semialgebraic optimization (with A.D. Ioffe, A.S. Lewis)
SIAM J. Optim. 26(1):513534, 2016. 
Transversality and alternating projections for nonconvex sets (with A.D. Ioffe, A.S. Lewis)
Found. Comput. Math. 15(6):16371651, 2015. 
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):13601380, 2015. 
Quadratic growth and critical point stability of semialgebraic functions (with A.D. Ioffe)
Math. Program. Ser. A., 153(2):635653, 2015. 
Projection methods for quantum channel construction (with C.K. Li, D.C. Pelejo, Y.L. Voronin, H. Wolkowicz)
Quantum Inf. Process., 14(8): 30753095, 2015. 
Extreme point inequalities and geometry of the rank sparsity ball (with S.A. Vavasis, H. Wolkowicz)
Math. Program. Ser. A, 152(12): 521544, 2015. 
Coordinate shadows of semidefinite and Euclidean distance matrices (with G. Pataki, H. Wolkowicz)
SIAM J. Optim., 25(2): 11601178, 2015. 
Clarke subgradients for directionally Lipschitzian stratifiable functions (with A.D. Ioffe, A.S. Lewis)
Math. Oper. Res. 40(2): 328349, 2015. 
Curves of descent (with A.D. Ioffe, A.S. Lewis)
SIAM J. Control and Optim., 53(1): 114138, 2015. 
Approximating functions on stratified sets (with M. Larsson)
Trans. Amer. Math. Soc. 367, 725749, 2015. 
Orbits of geometric descent (with A. Daniilidis, A.S. Lewis)
Canad. Math. Bull., 58(1): 4450, 2015. 
Orthogonal invariance and identifiability (with A. Daniilidis, A.S. Lewis)
SIAM J. Matrix Anal. Applic., 35(2): 580598, 2014. 
Optimality, identifiability, and sensitivity (with A.S. Lewis)
Math. Program. Ser. A, (147)1: 467498, 2014. Long version 
Secondorder growth, tilt stability, and metric regularity of the subdifferential (w/ B.S. Mordukhovich, T.T.A. Nghia)
J. Convex Anal., 21(4): 11651192, 2014. 
Semialgebraic functions have small subdifferentials (with A.S. Lewis)
Math. Program. Ser. B., 140(1): 529, 2013. 
Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential (with A.S. Lewis)
SIAM J. Optim., 23(1): 256267, 2013. 
The dimension of semialgebraic subdifferential graphs (with A.S. Lewis, A.D. Ioffe)
Nonlinear Analysis, 75(3):12311245, 2012. 
Generic nondegeneracy in convex optimization (with A.S. Lewis)
Proc. Amer. Math. Soc. 139, 25192527, 2011.
Ph.D. thesis
Invited Research Talks
 Robust algorithms for stochastic optimization, Machine Learning and Optimization, Microsoft Research, Redmond, WA, Aug. 2019.
 Convergence Rates of Stochastic Algorithms in Nonsmooth Nonconvex Optimization, Mathematics of Data and Decisions (MADD), UC Davis, CA, Feb. 2019.
 Convergence Rates of Stochastic Algorithms in Nonsmooth Nonconvex Optimization, Computational and Applied Mathematics Colloquium, U. Chicago, IL, Oct. 2018.
 Stochastic methods for nonsmooth nonconvex optimization, Variational Analysis and Applications, Erice, Sicily, Aug. 2018.
 Convergence rates of stochastic algorithms for nonsmooth nonconvex problems, Modern Trends in Nonconvex Optimization for Machine Learning, ICML 2018 Workshop, Stockholm, Sweden, Jul. 2018.
 Stochastic methods for nonsmooth nonconvex optimization, Nonconvex Formulations and Algorithms in Data Sciences, U. Wisconsin Madison, WI, Aug. 2018.
 Stochastic subgradient method converges on tame functions, ISMP 2018, Bordeaux, France, Jul. 2018.
 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
 Taylorlike models in nonsmooth optimization, SIAM Conf. on Optimization, Vancouver, Canada, May 2017. Slides
 Efficiency of innerouter 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, DIMCMM 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, UWPIMS 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