Preprints/Articles in review:

1. Aiming towards the minimizers: fast convergence of SGD for overparametrized problems (with C. Liu, M. Belkin, D. Davis, Y.-A. Ma) Manuscript, 2022. 

2. Stochastic approximation with decision-dependent distributions: asymptotic normality and optimality (with J. Cutler, M. Diaz) Manuscript, 2022. 

3. Active manifolds, stratifications, and convergence to local minima in nonsmooth optimization (with D. Davis, L. Jiang) Manuscript, 2021. 

4. Asymptotic normality and optimality in nonsmooth stochastic approximation (with D. Davis, L. Jiang) Manuscript, 2021. 

5. Flat minima generalize for low-rank matrix recovery (with L. Ding, M. Fazel, Z. Harchaoui), Manuscript, 30 pages, 2022.

Journal publications (accepted or appeared):

1. Stochastic algorithms with geometric step decay converge linearly on sharp functions (with D. Davis, V. Charisopoulos) To appear in Math. Program., 2023. Code

2. The slope robustly determines convex functions (with A. Daniilidis) To appear in  Proc. Amer. Math. Soc., 2023. 

3. Stochastic optimization under time drift: iterate averaging, step decay, and high probability guarantees (with J. Cutler, Z. Harchaoui) To appear in J. Mach. Learn. Res., 2022. 

4. Multiplayer performative prediction: learning in decision dependent games (with A. Narang, E. Faulkner, M. Fazel, L.J. Ratliff) To appear in J. Mach. Learn. Res., 2022. 

5. Stochastic optimization with decision-dependent distributions (with L. Xiao), To appear in Math. Oper. Res., 2022.

6. Conservative and semismooth derivatives are equivalent for semialgebraic maps (with D. Davis) Set-valued and Variational Analysis, pp.1-11, 2021.

7. Proximal methods avoid active strict saddles of weakly convex functions (with D. Davis) Found. Comput. Math., pp.1-46, 2021.

8. From low probability to high confidence in stochastic convex optimization (with D. Davis, L. Xiao, J. Zhang) J. Mach. Learn. Res., 22(49):1-38, 2021.

9. Composite optimization for robust rank one bilinear sensing (with V. Charisopoulos, D. Davis, M. Diaz) IMA Inf. Inference, 10(2), 333-396,  2021. Code

10. Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence (with V. Charisopoulos, Y. Chen, D. Davis, M. Diaz, L. Ding) Found. Comput. Math., 1-89, 2020. Code

11. Pathological subgradient dynamics (with A. Daniilidis) SIAM J. Optim.,  30(2), 1327-1338, 2020. 

12. Graphical convergence of subgradients in nonconvex optimization and learning (with D. Davis) To appear in Math. Oper. Res.,  2020.

13. Stochastic subgradient method converges on tame functions (with D. Davis, S. Kakade, and J.D. Lee) Found. Comput. Math. 20(1):119-154, 2020. Finalist for the Best Paper Prize for Young Researchers in Continuous Optimization (2019)

14. Level-set methods for convex optimization (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and S. Roy) Math. Program. Ser. B, 174(1-2): 359-390, 2019.

15. Local linear convergence for inexact alternating projections on nonconvex sets (with A.S. Lewis) Special issue in honor of Alex Ioffe, Vietnam J. Math., 47(3):669-681, 2019.

16. Stochastic model-based minimization of weakly convex functions (with D. Davis) SIAM J. Optim., no. 1, 207-239, 2019. This is the combination of the two arXiv preprints arXiv:1802.02988 and arXiv:1803.06523.  Recipient of the SIAG/OPT Best Paper Prize (2023) & INFORMS Optimization Society Young Researchers Prize (2019)

17. The nonsmooth landscape of phase retrieval (with D. Davis and C. Paquette) IMA J. Numer. Anal., 40(4):2652-2695, 2018.

18. Efficiency of minimizing compositions of convex functions and smooth maps (with C. Paquette) Math. Program., 178(1-2): 503-558, 2019.

19. Subgradient methods for sharp weakly convex functions (with D. Davis, K.J. MacPhee, and C. Paquette) J. Optim. Theory App. 179(3):962-982, 2018.

20. Foundations of gauge and perspective duality (with A.Y. Aravkin, J.V. Burke, M.P. Friedlander, and K. MacPhee) SIAM J. Optim. 28(3):2406-2434, 2018.

21. Error bounds, quadratic growth, and linear convergence of proximal methods (with A.S. Lewis) Math. Oper. Res. 43(3):919-948, 2018.

22. Efficient quadratic penalization through the partial minimization technique (with A.Y. Aravkin and T. van Leeuwen) IEEE Trans. Automat. Contr. 63(7):2131-2138, 2018.

23. An optimal first order method based on optimal quadratic averaging (with M. Fazel and S. Roy), SIAM J. Optim. 28(1):251-271, 2018. Code 

24. Variational analysis of spectral functions simplified (with C. Paquette) J. Convex Anal. 25(1):119-134, 2018.

25. The Euclidean distance degree of orthogonally invariant matrix varieties (with H.-L. Lee, G. Ottaviani, R.R. Thomas) Israel J. Math. 221(1):291-316 2017.

26. Sweeping by a tame process (with A. Daniilidis) Ann. Inst. Fourier (Grenoble) 67(5):2201-2223, 2017.

27. Noisy Euclidean distance realization: robust facial reduction and the Pareto frontier (with N. Krislock, Y.-L. Voronin, and H. Wolkowicz), SIAM J. Optim. 27(4):2301-2331, 2017. Code

28. 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.

29. Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria (with A.D. Ioffe and A.S. Lewis) Math. Program. Ser. A, 185, 357-383, 2021.

30. Generic minimizing behavior in semi-algebraic optimization (with A.D. Ioffe, A.S. Lewis) SIAM J. Optim. 26(1):513-534, 2016.

31. Transversality and alternating projections for nonconvex sets (with A.D. Ioffe, A.S. Lewis) Found. Comput. Math. 15(6):1637-1651, 2015.

32. 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.

33. Quadratic growth and critical point stability of semi-algebraic functions (with A.D. Ioffe) Math. Program. Ser. A., 153(2):635-653, 2015.

34. 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.

35. 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.

36. Coordinate shadows of semi-definite and Euclidean distance matrices (with G. Pataki, H. Wolkowicz) SIAM J. Optim., 25(2): 1160-1178, 2015.

37. Clarke subgradients for directionally Lipschitzian stratifiable functions (with A.D. Ioffe, A.S. Lewis) Math. Oper. Res. 40(2): 328-349, 2015.

38. Curves of descent (with A.D. Ioffe, A.S. Lewis) SIAM J. Control and Optim., 53(1): 114-138, 2015.

39. Approximating functions on stratified sets (with M. Larsson) Trans. Amer. Math. Soc. 367, 725-749, 2015.

40. Orbits of geometric descent (with A. Daniilidis, A.S. Lewis) Canad. Math. Bull., 58(1): 44-50, 2015.

41. Orthogonal invariance and identifiability (with A. Daniilidis, A.S. Lewis) SIAM J. Matrix Anal. Applic., 35(2): 580-598, 2014.

42. Optimality, identifiability, and sensitivity (with A.S. Lewis) Math. Program. Ser. A, (147)1: 467-498, 2014. Long version

43. 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.

44. Semi-algebraic functions have small subdifferentials (with A.S. Lewis) Math. Program. Ser. B., 140(1): 5-29, 2013.

45. Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential (with A.S. Lewis) SIAM J. Optim., 23(1): 256-267, 2013.

46. The dimension of semi-algebraic subdifferential graphs (with A.S. Lewis, A.D. Ioffe) Nonlinear Analysis, 75(3):1231-1245, 2012.

47. Generic nondegeneracy in convex optimization (with A.S. Lewis) Proc. Amer. Math. Soc. 139, 2519-2527, 2011.

Conference Proceedings:

1. A gradient sampling algorithm with complexity guarantees for Lipschitz functions in high and low dimensions (with D. Davis, Y.T. Lee, S. Padmanabhan, G. Ye) Proceedings of  NeurIPS (Oral presentation), 2022.

2. Learning in Stochastic Monotone Games with Decision-Dependent Data  (A. Narang, E. Faulkner, D. Drusvyatskiy, M. Fazel, L.J. Ratliff) Proceedings of  AISTATS, PMLR:5891-5912,2022.

3. Decision-dependent risk minimization in geometrically decaying dynamic environments (M. Ray, L.J. Ratliff, D. Drusvyatskiy, M. Fazel) AAAI Conference on Artificial Intelligence, 2022.

4. Stochastic optimization under time drift: iterate averaging, step decay, and high probability guarantees (J. Cutler, D. Drusvyatskiy, Z. Harchaoui) Proceedings of  NeurIPS, PMLR:11859-11869 2021.

5.  High probability guarantees for stochastic convex optimization (D. Davis, D. Drusvyatskiy) Proceedings of   COLT, PMLR:1411-1427, 2020. 

6. Iterative Linearized Control: Stable Algorithms and Complexity Guarantees (V. Roulet, S. Srinivasa, D. Drusvyatskiy, Z. Harchaoui) Proceedings of ICML, PMLR:5518-5527, 2019.

7.  Catalyst for Gradient-based Nonconvex Optimization (C. Paquette, H. Lin, D. Drusvyatskiy, J. Mairal, Z. Harchaoui) Proceedings of   AISTATS, PMLR 84:613-622, 2018.

Expository Writing:

1. Subgradient methods under weak convexity and tame geometry (with D. Davis) SIAG/OPT Views and News, Vol. 28, No. 1, pp 1-10, 2020.

2. The proximal point method revisited SIAG/OPT Views and News, Vol. 26, No. 1, 2018.

3. The many faces of degeneracy in conic optimization (with H. Wolkowicz) Foundations and Trends in Optimization, Vol. 3, No. 2, pp 77-170, 2017.

4. 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.

Thesis:

Slope and geometry in variational mathematics Finalist for the A. W. Tucker Prize (2015)

Supplementary technical reports:

1. Stochastic model-based minimization under high-order growth (with D. Davis and K.J. MacPhee), Manuscript, 30 pages, 2018, appears as a chapter in K.J. MacPhee's thesis.

2. Complexity of finding near-stationary points of convex functions stochastically (with D. Davis), Short note,  9 pages, 2018