Zhaosong Lu

Professor
Department of Industrial and Systems Engineering
University of Minnesota

Phone: (612) 626-9431
Email: zhaosong@umn.edu

• Theoretical foundations and algorithm development for hierarchical, distributed, robust, and stochastic optimization
• Intersections of optimization, machine learning, and statistics for AI safety and high-dimensional data analysis
• Development of novel and efficient methods for large-scale optimization in AI and machine learning

• IE 8564: Optimization for machine learning, Fall 2022-2024.
• IE 8534: Advanced topics in numerical optimization, Spring 2023.
• IE 8534: Advanced topics in optimization for machine learning, Fall 2020, 2021.
• IE 5561: Analytics and data-driven decision making, Spring 2021-2024.
• IE 5080: Optimization models and methods for machine learning, Spring 2020.

• Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees (with S. Mei and Y. Xiao), submitted.
• A first-order method for nonconvex-strongly-concave constrained minimax optimization (with S. Mei), submitted.
• Solving bilevel optimization via sequential minimax optimization (with S. Mei), submitted.
• A first-order augmented Lagrangian method for constrained minimax optimization (with S. Mei), accepted by Mathematical Programming.
• Single-loop stochastic algorithms for difference of max-structured weakly convex functions (with Q. Hu, Q. Qi and T. Yang), accepted by NeurIPS, 2024.
• Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity (with S. Mei), To appear in Mathematics of Operations Research, 2024.
• A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization (with C. He and H. Huang), To appear in Computational Optimization and Applicationsem, 2024.
• Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery (with L. Huang, X. Liu, J. Lu, M. Ng and H. Zhu), Advances in Computational Mathematics, 50:75, 2024.
• First-order penalty methods for bilevel optimization (with S. Mei), SIAM Journal on Optimization, 34(2):1937-1969, 2024.
• Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient (with S. Mei), SIAM Journal on Optimization, 33(3): 2275-2310, 2023.
• Generalized-smooth nonconvex optimization is as efficient as smooth nonconvex optimization (with Z. Chen, Y. Liang and Y. Zhou), Proceedings of International Conference on Machine Learning, 2023.
• A Newton-CG based augmented Lagrangian method for finding a second-order stationary point of nonconvex equality constrained optimization with complexity guarantees (with C. He and T. K. Pong), SIAM Journal on Optimization, 33(3):1734-1766, 2023.
• A Newton-CG based barrier method for finding a second-order stationary point of nonconvex conic optimization with complexity guarantees (with C. He), SIAM Journal on Optimization, 33(2): 1191-1222, 2023.
• Iteration complexity of first-order augmented Lagrangian methods for convex conic programming (with Z. Zhou), SIAM Journal on Optimization, 33(2):1159-1190, 2023.
• A parameter-free conditional gradient method for composite minimization under Hölder condition (with C. He and M. Ito), Journal of Machine Learning Research, 24:1-34, 2023.
• Exactly uncorrelated sparse principal component analysis (with O. Kwon and H. Zou), Journal of Computational and Graphical Statistics, 33(1):231-241, 2024.
• A nonlocal Kronecker-basis-representation method for low-dose CT sinogram recovery (with H. Hu, L. Li, X. Liu, J. Lu, Y. Zou and K. Zu), Journal of Computational Mathematics, 42(4):1080-1108, 2024.
• A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising (with W. Hu, Q. Jiang, J. Lu, H. Pan, Z. Tu and H. Zhu), Inverse Problems, 39: 065003, 2023.
• Exact penalization for cardinality and rank constrained optimization problems via partial regularization (with X. Li and S. Xiang), Optimization Methods and Software, 38(2):412-433, 2023.
• FastPicker: Adaptive independent two-stage video-to-video summarization for efficient action recognition (with S. Alfasly, Z. Al-Huda, C. K. Chui, Q. Jiang, J. Lu and C. Xu), Neurocomputing, 516: 231-244, 2023.
• Penalty and augmented Lagrangian methods for a class of structured nonsmooth DC constrained DC programming (with Z. Sun and Z. Zhou), Mathematics of Operations Research, 47(3):2260-2285, 2022.
• Convergence rate analysis of a sequential convex programming method with line search for a class of constrained difference-of-convex optimization problems (with P. Yu and T. K. Pong), SIAM Journal on Optimization, 31(3): 2024–2054, 2021.
• An exact penalty method for semidefinite-box constrained low-rank matrix optimization problems (with X. Chen, Y.-H. Dai and T. Liu), IMA Journal of Numerical Analysis, 40(1):563-586, 2020.
• Nonmonotone enhanced proximal DC algorithms for a class of structured nonsmooth DC programming (with Z. Zhou), SIAM Journal on Optimization, 29(4):2725-2752, 2019.
• Enhanced proximal DC algorithms with extrapolation for a class of structured nonsmooth DC minimization (with Z. Sun and Z. Zhou), Mathematical Programming, 176(1-2): 369-401, 2019.
• $l_0$-Minimization methods for image restoration problems based on wavelet frames (with X. Li, J. Lu, K. Qiao and Y. Zou), Inverse Problems, 35(6), 2019.
• Sparse recovery via partial regularization: models, theory and algorithms (with X. Li), Mathematics of Operations Research, 43(4): 1290-1316, 2018.
• Generalized conjugate gradient methods for $\ell_1$ regularized convex quadratic programming with finite convergence (with X. Chen), Mathematics of Operations Research, 43(1): 275-303, 2018.
• A framelet algorithm for de-blurring images corrupted by multiplicative noise (with J. Lu, L. Shen, C. Xu, H. Yang and Z. Yang), Applied Mathematical Modelling, 62: 51-61, 2018.
• $\ell_p$ regularized low-rank approximation via iterative reweighted singular value minimization (with J. Lu and Y. Zhang). Computational Optimization and Applications, 68(3):619-642, 2017.
• Randomized block proximal damped Newton method for composite self-concordant minimization, SIAM Journal on Optimization, 27(3), 1910-1942, 2017.
• A randomized nonmonotone block proximal gradient method for a class of structured nonlinear programming (with L. Xiao), SIAM Journal on Numerical Analysis, 55(6): 2930-2955, 2017.
• An augmented Lagrangian method for non-Lipschitz nonconvex programming (with X. Chen, L. Guo and J. Ye), SIAM Journal on Numerical Analysis, 55(1), 168-193, 2017.
• Penalty methods for a class of non-Lipschitz optimization problems (with X. Chen and T.K. Pong), SIAM Journal on Optimization, 26(3): 1465-1492, 2016.
• An efficient optimization approach for cardinality-constrained index tracking problems (with F. Xu and Z. Xu), Optimization Methods and Software, 31(2):258-271, 2016.
• An accelerated randomized proximal coordinate gradient method and its application to regularized empirical risk minimization (with Q. Lin and L. Xiao), SIAM Journal on Optimization, 25(4): 2244-2273, 2015.
• A proximal gradient method for ensemble density functional theory (with D. Klockner, M. Ulbrich, Z. Wen and C. Yang), SIAM Journal on Scientific Computing, 37(4): A1975-A2002, 2015.
• Fused multiple graphical lasso (with X. Shen, P. Wonka, S. Yang and J. Ye), SIAM Journal on Optimization, 25(2): 916-943, 2015.
• Orthogonal rank-one matrix pursuit for matrix completion (with M. Lai, Z. Wang and J. Ye), SIAM Journal on Scientific Computing, 37(1): A488-A514, 2015.
• On the complexity analysis of randomized block-coordinate descent methods (with L. Xiao), Mathematical Programming, 152(1): 615-642, 2015.
• Penalty decomposition methods for rank minimization (with X. Li and Y. Zhang), Optimization Methods and Software, 30(3): 531-558, 2015.
• An accelerated proximal coordinate gradient method (with Q. Lin and L. Xiao), Proceedings of Neural Information Processing Systems (NIPS), 3059-3067, 2014.
• Orthogonal rank-one matrix pursuit for matrix completion (with M. Lai, Z. Wang and J. Ye), Proceedings of The 31st International Conference on Machine Learning, 91-99, 2014.
• Iterative reweighted minimization methods for $l_p$ regularized unconstrained nonlinear programming, Mathematical Programming, 147(1-2): 277-307, 2014.
• Iterative hard thresholding methods for $l_0$ regularized convex cone programming, Mathematical Programming, 147(1-2): 125-154, 2014.
• Sparse Approximation via penalty decomposition methods (with Y. Zhang), SIAM Journal on Optimization, 23(4):2448-2478, 2013.
• Computing optimal experimental designs via interior point method (with T.K. Pong), SIAM Journal on Matrix Analysis and Applications, 34(4): 1556-1580, 2013.
• FeaFiner: biomarker identification from medical data through feature generalization and selection (with J. Sun, L. Yuan, F. Wang, J. Ye and J. Zhou), Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD 2013), 1034-1042, 2013.
• A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems (with P. Gong, J. Huang, J. Ye and C. Zhang), Proceedings of International Conference on Machine Learning, 28(2):37-45, 2013.
• $l_0$ minimization for wavelet frame based image restoration (with B. Dong and Y. Zhang), Mathematics of Computation, 82:995-1015, 2013.
• Assessing the value of dynamic pricing in network revenue management (with D. Zhang), INFORMS Journal on Computing, 25(1):102-115, 2013.
• Primal-dual first-order methods for a class of cone programming , Optimization Methods and Software, 28(6):1262-1281, 2013.
• An Alternating direction method for finding Dantzig selectors (with T.K. Pong and Y. Zhang), Computational Statistics and Data Analysis, 56(12):4037-4046, 2012.
• An augmented Lagrangian approach for sparse principal component analysis (with Y. Zhang), Mathematical Programming, 135:149-193, 2012.
• Convex optimization methods for dimension reduction and coefficient estimation in multivariate linear regression (with R.D.C. Monteiro and M. Yuan), Mathematical Programming, 131:163-194, 2012.
• Penalty decomposition emthods for rank minimization (with Y. Zhang), Proceedings of Neural Information Processing Systems (NIPS), 46-54, 2011.
• Minimizing condition number via convex programming (with T.K. Pong), SIAM Journal on Matrix Analysis and Applications, 32(4):1193-1211, 2011.
• A computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set, Mathematical Programming, 126(1):193-201, 2011.
• Primal-dual first-order methods with $O(1/\epsilon)$ iteration-complexity for cone programming (with G. Lan and R.D.C. Monteiro), Mathematical Programming, 126(1):1-29, 2011.
• Robust Portfolio selection based on a joint ellipsoidal uncertainty Set, Optimization Methods and Software, 26(1): 89-104, 2011.
• Adaptive first-order methods for general sparse inverse covariance selection, SIAM Journal on Matrix Analysis and Applications, 31(4):2000-2016, 2010.
• Smooth optimization approach for sparse covariance selection, SIAM Journal on Optimization, 19(4):1807-1827, 2009.
• An iterative solver-based long-step nfeasible primal-dual path-following algorithm for convex QP based on a class of preconditioners (with R.D.C. Monteiro and J. O'Neal), Optimization Methods and Software, 24(1):123-143, 2009.
• Diagonal Quadratic approximation for parallelization of analytical target cascading (with Y. Li and J.J. Michalek), ASME Journal of Mechanical Design, 130(5), 2008.
• Dimension reduction and coefficient estimation in the multivariate linear regression (with A. Ekici, R.D.C. Monteiro and M. Yuan), Journal of the Royal Statistical Society, Series B, 69(3):329-346, 2007.
• Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming (with R.D.C. Monteiro), Optimization Methods and Software, 22(5):849-870, 2007.
• A modified nearly exact method for solving low-rank trust region subproblem (with R.D.C. Monteiro), Mathematical Programming,109(2):385-411, 2007.
• Large-scale semidefinite programming via saddle point mirror-prox algorithm (with R.D.C. Monteiro and A.S. Nemirovski), Mathematical Programming,109(2):211-237, 2007.
• An iterative solver-based infeasible primal-dual path-following algorithm for convex quadratic programming (with R.D.C. Monteiro and J. O'Neal), SIAM Journal on Optimization, 17(1):287-310, 2006.
• A Note on the Local Convergence of a predictor-corrector interior-point algorithm for the semidefinite linear complementarity problem based on the Alizadeh-Haeberly-Overton search direction (with R.D.C. Monteiro), SIAM Journal on Optimization, 15(4):1147-1154, 2005.
• optimal solutions for the closest-string problem via integer programming (with C. Meneses, C.A. Olivera and P.M. Pardalos), INFORMS Journal on Computing, 16:419-429, 2004.
• Error bounds and limiting behavior of weighted paths associated with the SDP map $X^{1/2}SX^{1/2}$ (with R.D.C. Monteiro), SIAM Journal on Optimization, 15(2):348-374, 2004.

• Optimization over sparse symmetric sets via a nonmonotone projected gradient method.
• Sequential convex programming methods for a class of structured nonlinear programming.
• Error bounds for first- and second-order approximations of eigenvalues and singular values (with T. K. Pong).

Editorial Service

Current and Former Ph.D. Students at UMN