About me:
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 semialgebraic 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.Courses
 Spring, 2018: MATH 124B/C (Calculus with Analytic Geometry I).
 Winter, 2018: MATH 408 (Nonlinear Optimization).
 Winter, 2017: MATH 408 (Nonlinear Optimization).
 Winter, 2017: MATH 581 A (Convex Analysis).
 Autumn, 2016: MATH 124D/E (Calculus with Analytic Geometry I)
 Spring, 2016: AMATH/MATH 516 (Numerical Optimization).
 Winter, 2016: MATH 408 (Nonlinear Optimization).
 Autumn, 2015: MATH 581 D (Convex Analysis).
 Spring, 2015: AMATH/MATH 516 (Numerical Optimization).
Preprints/Articles in review

Stochastic subgradient method converges
on tame functions (with D. Davis, S. Kakade, and J.D. Lee)
Manuscript, 32 pages, 2018. 
Stochastic modelbased minimization of weakly convex functions (with D. Davis)
Manuscript, 10 pages, 2018. 
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 nearstationary points of convex functions stochastically 
Subgradient methods for sharp weakly convex functions (with D. Davis, K.J. MacPhee, and C. Paquette)
Manuscript, 16 pages, 2018. 
The nonsmooth landscape of phase retrieval (with D. Davis and C. Paquette)
Manuscript, 42 pages, 2017. 
Catalyst acceleration for gradientbased nonconvex optimization (w/ C. Paquette, H. Lin, J. Mairal, Z. Harchaoui)
Preprint, 30 pages, 2017. 
Efficiency of minimizing compositions of convex functions and smooth maps (with C. Paquette)
Manuscript, 38 pages, 2016. 
Nonsmooth optimization using Taylorlike models: error bounds, convergence, and termination criteria (with A.D. Ioffe and A.S. Lewis)
Manuscript, 23 pages, 2016. 
Levelset methods for convex optimization (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and S. Roy)
Manuscript, 38 pages, 2016.
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)

Foundations of gauge and perspective duality (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and K. MacPhee)
To appear in SIAM J. Optim., 2018. 
Error bounds, quadratic growth, and linear convergence of proximal methods (with A.S. Lewis)
To appear in Math. Oper. Res. 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. 
Efficient quadratic penalization through the partial minimization technique (with A.Y. Aravkin and T. van Leeuwen)
To appear in IEEE Trans. Automat. Contr., 2017. 
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. 
Sweeping by a tame process (with A. Daniilidis)
To appear in Ann. Inst. Fourier (Grenoble), 2016. 
Variational analysis of spectral functions simplified (with C. Paquette)
J. Convex Anal. 25(1), 2018. 
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. 
A note on alternating projections for illposed semidefinite feasibility problems (with G. Li and H. Wolkowicz)
Math. Program. 162(12):537548, 2017. 
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
 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