Publications

See Dr. Lan’s Google Scholar page for a more complete list. 

Books

Journal Papers (* student or post-doc co-authors)

  1. G. Lan and Y. Li*, A Novel Catalyst Scheme for Stochastic Minimax Optimization, released on arXiv, November 2023, submitted for publication, January 2024.
  2. G. Lan, Y. Ouyang and Z. Zhang, Optimal and parameter-free gradient minimization methods for convex and nonconvex optimization, released on arXiv, October 2023, submitted for publication, December 2023.
  3. T. Li* and G. Lan, A simple uniformly optimal method without line search for convex optimization, released on arXiv, October 2023, submitted for publication, October 2023.
  4. S. Ilandarideva*, A. Juditsky, G. Lan and T. Li*, Accelerated stochastic approximation with state-dependent noise, released on arXiv, July 2023, submitted for publication, July 2023.
  5. Y. Li*, G. Lan and T. Zhao, First-order Policy Optimization for Robust Markov Decision Process, released on arXiv, September 2022, submitted for publication, June 2023.
  6. G. Lan and A. Shapiro, Numerical methods for convex multistage stochastic optimization, released on arXiv, March 2023, submitted for publication, March 2023.
  7. Y. Li* and G. Lan, Policy mirror descent inherently explores action space, released on arXiv, March 2023; submitted for publication, March 2023.
  8. C. Ju* and G. Lan, Dual dynamic programming for stochastic programs over an infinite horizon, released on arXiv, March 2023; submitted for publication.
  9. C. Ju*, G. Kotsalis and G. Lan, A model-free first-order method for linear quadratic regulator with Õ(1/ε) sampling complexity, released on arXiv, November 2022; submitted for publication, February 2023.
  10. G. Lan, Policy optimization over general state and action space, released on arXiv, November 2022; submitted for publication, January 2023.
  11. Z. Zhang* and G. Lan, Solving Convex Smooth Function Constrained Optimization Is Almost As Easy As Unconstrained Optimization, submitted for publication, November 2022.
  12. Yi. Cheng*, G. Lan and H. E. Romeijn, Function constrained optimization for risk aversion and sparsity control, submitted for publication, November 2022.
  13. T. Li*, F. Wu* and G. Lan, Stochastic first-order methods for average-reward Markov decision processes, May 2022, submitted for publication, September 2022.
  14. D. Boob, Q. Deng and G. Lan, Level Constrained First Order Methods for Function Constrained Optimization, May 2022, submitted to Mathematical Programming; accepted for publication, January 2024.
  15. G. Lan and Z. Zhang*, Optimal Methods for Risk Averse Distributed Optimization, March 2022, submitted to SIAM Journal on Optimization; accepted for publication, November 2022.
  16. S. Yang, X. Li and G. Lan, Data-Driven Minimax Optimization with Expectation Constraints, February 2022, submitted to Operations Research, accepted for publication, November 2023.
  17. Y. Li*, G. Lan and T. Zhao Homotopic Policy Mirror Descent: Policy Convergence, Implicit Regularization, and Improved Sample Complexity, released on arXiv, January 2022; submitted to Mathematical Programming, January 2023; accepted for publication, July 2023.
  18. G. Lan, Y. Li* and T. Zhao, Block policy mirror descent, January 2022, submitted to SIAM Journal on Optimization; accepted for publication, April 2023.
  19. T. Li*, G. Lan and A. Pananjady, Accelerated and instance-optimal policy evaluation with linear function approximation, December 2021, submitted to SIAM Journal on Mathematics of Data Science; accepted for publication, November 2022.
  20. G. Lan and Y. Ouyang, Mirror-prox sliding methods for solving a class of monotone variational inequalities, November 2021, submitted for publication.
  21. G. Lan and Y. Zhou, Asynchronous decentralized accelerated stochastic gradient descent, IEEE Journal on Selected Areas in Information Theory, accepted for publication, May 2021.
  22. G. Lan, Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes, submitted to Mathematical Programming, February 2021; revision submitted, October 2021; accepted for publication, April 2022.
  23. G. Lan, Y. Ouyang and Y. Zhou, Graph Topology Invariant Gradient and Sampling Complexity for Decentralized and Stochastic Optimization, submitted to SIAM Journal on Optimization, January 2021; revision submitted, December 2021; accepted for publication, February 2023.
  24. Z. Zhang* and G. Lan, Optimal Algorithms for Convex Nested Stochastic Composite Optimization, submitted for publication, November 2020; revision submitted, June 2022.
  25. G. Kotsalis*, G. Lan and T. Li*, Simple and Optimal Methods for Stochastic Variational Inequalities, II: Markovian Noise and Policy Evaluation in Reinforcement Learning, submitted to SIAM Journal on Optimization, November 2020; accepted for publication, January 2022; published on v.32(2), pp.1120-1155.
  26. G. Kotsalis*, G. Lan and T. Li*, Simple and Optimal Methods for Stochastic Variational Inequalities, I: Operator Extrapolation, submitted to SIAM Journal on Optimization, November 2020; accepted for publication, May 2022; published on v. 32(2), pp. 2041-2073, 2022.
  27. G. Lan, H. E. Romeijn and Z. Zhou*, Conditional Gradient Methods for Convex Optimization with General Affine and Nonlinear Constraints, submitted to SIAM Journal on Optimization,July 2020; accepted for publication, Feb. 2021; published on v.31(3), pp. 2307-2339, 2021.
  28. G. Kotsalis*, G. Lan and A. Nemirovski, Convex Optimization for Finite Horizon Robust Covariance Control of Linear Stochastic Systems, submitted for publication, July 2020; SIAM Journal on Control and Optimization, v.59(1), pp.296-319, 2021.
  29. B. Zhang*, G. Kotsalis*, J. Khan*, Z. Xiong*, T. Igou*, G. Lan and Y. Chen, Backwash Sequence Optimization of a Pilot-Scale Ultrafiltration Membrane System Using Data-Driven Modeling for Parameter Forecasting, Journal of Membrane Science, Volume 612 (15), 2020.
  30. Z. Xu, H. Zhang*, Y. Xu* and G. Lan, A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems, submitted to Mathematical programming, June 2020; second revision submitted, July 2022; accepted for publication, January 2023.
  31. G.Lan, Complexity of Stochastic Dual Dynamic Programming, submitted for publication, December 2019; Mathematical Programming, v. 191, pp. 717-754, 2022.
  32. D. Boob*, Q. Deng and G. Lan, Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization, submitted for publication, October 2019. An initial version entitled “Proximal Point Methods for Optimization with Nonconvex Functional Constraints”  was released on arXiv in August 2019; Mathematical Programming, accepted for publication, October 2021, published: v. 197, pp.215-279, 2023.
  33. Z. Zhang*, S. Ahmed and G.Lan, Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support, submitted for publication, September 2019, SIAM Journal on Optimization, accepted for publication, March 2021, published on v.31(3), pp.1690-1721, 2021.
  34. *Q. Wang, Z. Wen, G. Lan and Y. Yuan, Complexity Analysis for Optimization Methods, Review Paper, SCIENTIA SINICA Mathematica, 2020.
  35. H. Bao*, Z. Zhou*, G Kotsalis*, G Lan, Z Tong, Lignin Valorization Process Control under Feedstock Uncertainty through a Dynamic Stochastic Programming Approach, submitted for publication, April 2019; Reaction Chemistry & Engineering, DOI 10.1039/C9RE00176J, 2019.
  36. D. Boob*, S. Dey and G. Lan, Complexity of Training Relu Neural Network, submitted for publication, September 2018, Discrete Optimization, accepted for publication, October 2020.
  37. Z. Wang*, Y. Zhou*, Y. Liang, and G. Lan, A Note on Inexact Gradient Hessian Condition for Cubic Regularized Newton’s Method, submitted for publication, August 2018; Operations Research Letters, Volume 47, Issue 2, Pages 146-149, 2019.
  38. G. Lan and Y. Yang*, Accelerated Stochastic Algorithms for Nonconvex Finite-sum and Multi-block Optimization, submitted for application, May 2018; SIAM Journal on Optimization, accepted for publication, August 2019.
  39. G. Lan and Y. Zhou*, Random gradient extrapolation for distributed and stochastic optimization, submitted for publication, November 2017; SIAM Journal on Optimization, 28(4), 2753-2782, 2018.
  40. G. Lan and Z. Zhou*, Dynamic Stochastic Approximation for Multi-stage Stochastic Optimization, submitted for publication, October 2017, Mathematical Programming, accepted for publication, March 2020, published on v.187, pp.487–532, 2021.
  41. C. Dang*, G. Lan and Z. Wen, “Linearly Convergent First-order Algorithms for Semidefinite Programming“, Journal of Computational Mathematics, Volume 35, Issue 4, pp 452-468, 2017 (evolves from a previous version released on arXiv in Sep. 2013).
  42. G. Lan, S. Lee* and Y. Zhou*, Communication-Efficient Algorithms for Decentralized and Stochastic Optimization, submitted for publication, January 2017; Mathematical Programming, accepted for publication, 2018.
  43. G. Lan and Y. Ouyang, “Accelerated Gradient Sliding for Structured Convex Optimization”, submitted for publication, September 2016, Computational Optimization and Applications, accepted for publication, 2022.
  44. G. Lan and Z. Zhou*, “Algorithms for Stochastic Optimization with Function or Expectation Constraints”, submitted for publication, August 2016, Computational Optimization and Applications, volume 76, pp 461–498, 2020, with some corrections made in arXiv.org, October 2020.
  45. G. Lan and Y. Zhou*, “An Optimal Randomized Incremental Gradient Method”, July 2015, updated and submitted for publication in October 2015; Mathematical Programming, accepted for publication, June 2017, Volume 171, Issue 1–2, pp 167–215, 2018.
  46. S. Ghadimi*, G. Lan, and H. Zhang, “Generalized Uniformly Optimal Methods for Nonlinear Programming”,  submitted for publication, August 2015; Journal of Scientific Computing, Volume 79, Issue 3, pp 1854–1881, 2019.
  47. Y. Chen, G. Lan, Y. Ouyang* and W. Zhang*, “Fast Bundle-level Methods for Unconstrained and Ball-constrained Convex Optimization“, submitted for publication, October 2015; Computational Optimization and Applications, Volume 73, Issue 1, pp 159–199, 2019.
  48. G. Lan and Y. Zhou*, “Conditional Gradient Sliding for Convex Optimization“, submitted for publication, October 20, 2014; SIAM Journal on Optimization,  accepted for publication, April 2016.
  49. C. D. Dang* and G. Lan, “Randomized First-order Methods for Saddle Point Optimization”,Technical Report, Department of Industrial and Systems Engineering, University of Florida, firstly released in September 2014, updated in October, 2015.
  50. A. Romich*, G. Lan, and J.C. Smith, “A Robust Sensor Covering and Communication Problem”, submitted for publication, August 3, 2014; Naval Research Logistics, Volume6, Issue7,pp582-594,2015.
  51. G. Lan, “Gradient Sliding for Composite Optimization”, submitted for publication, June 11, 2014; Mathematical Programming, Volume 159, Issue 1–2, pp 201–235, 2016.
  52. Y. Chen, G. Lan, and Y. Ouyang*, “Accelerated Schemes For A Class of Variational Inequalities“, submitted for publication, March 2014; Mathematical Programming, Series B, Volume 165, Issue 1, pp 113-149, 2017.
  53. Y. Ouyang*, Y. Chen, G. Lan, and E. Pasiliao, “An Accelerated Linearized Alternating Direction Method of Multipliers”, submitted for publication, Jan. 2014; SIAM Journal on Imaging Sciences, Vol. 8, No. 1, pp. 644–681, 2015.
  54. S. Ghadimi* and G. Lan, “Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming“,  submitted for publication, October 2013; Mathematical Programming, accepted for publication, February 2015, DOI: 10.1007/s10107-015-0871-8, Volume 156, Issue 1, pp 59–99, 2016.
  55. C. D. Dang* and G. Lan, “Stochastic Block Mirror Descent Methods for Nonsmooth and Stochastic Optimization“,  submitted for publication, Sep. 2013; SIAM Journal on Optimization, v. 25, n. 2m pp, 856-881,2015.
  56. Y. Chen, G. Lan, and Y. Ouyang*, “Optimal Primal-Dual Methods for a Class of Saddle Point Problems“, submitted for publication, Sep. 2013; SIAM Journal on Optimization, v 24 (4), 1779-1814, 2014.
  57. S.Ghadimi*, G. Lan, and H. Zhang, “Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization”, submitted for publication, August 2013; Mathematical Programming, accepted for publication, Nov. 2014, DOI: 10.1007/s10107-014-0846-1, Volume 155, Issue 1, pp 267-305, 2016.
  58. G. Lan, “The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle“, technical report, Department of Industrial and Systems Engineering, University of Florida, June 2013, updated in June 2014, included in my book “First-order and Stochastic Optimization Methods for Machine Learning“.
  59. A. Romich*, G. Lan, and J.C. Smith, “Algorithms for optimizing Placement of Stationary Monitors“, submitted for publication, 2012; IIE Transactions, accepted for publication, July 8, 2014, DOI: 0.1080/0740817X.2014, v.47, 1-21, 2015.
  60. C.D. Dang*, K. Dai, and G. Lan, “A Linearly Convergent First-order Algorithm for Total Variation Minimization in Image Processing”, submitted for publication, Oct. 2012; International Journal of Bioinformatics Research and Applications, 10 (1), 4-26, 2014. (A special issue for the International Conference on Computational Biomedicine in Gainesville, Florida, February 29 – March 2, 2012.)
  61. S. Ghadimi* and G. Lan, “Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming“, submitted for publication, June 2012; SIAM Journal on Optimization, 23(4), 2341–2368, 2013. (Extended report.) (This paper won the first place in the 2012 INFORMS Junior Faculty Interest Group (JFIG) paper competition.)
  62. C. D. Dang* and G. Lan, “On the Convergence Properties of Non-Euclidean Extragradient Methods for Variational Inequalities with  Generalized Monotone Operators“, submitted for publication, April 2012; Computational Optimization and Applications, accepted for publication, June 3, 2014, Volume 60(2), 277-310, 2015.
  63. G. Lan, “Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization”, submitted for publication, Dec. 2010, April 2011; Mathematical Programming, accepted for publication, Oct. 4, 2013, V149 (1):1–45, 2015.
  64. S. Ghadimi* and G. Lan, “Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, II: shrinking procedures and optimal algorithms”, submitted for publication, July 2010; SIAM Journal on Optimization, 23(4), 2061–2089, 2013.
  65. S. Ghadimi* and G. Lan, “Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, I: a generic algorithmic framework”, submitted for publication, July 2010; SIAM Journal on Optimization, V 22, 1469-1492, 2012.
  66. G. Lan and R.D.C. Monteiro, “Iteration-complexity of first-order augmented Lagrangian methods for convex programming“, submitted for publication, May 2009; Mathematical Programming, accepted for publication, December, 2014,  DOI 10.1007/s10107-015-0861-x, Volume 155, Issue 1, pp 511-547, 2016.
  67. G. Lan and R.D.C. Monteiro, “Iteration complexity of first-order penalty methods for convex programming”, submitted for publication, July 2008; Mathematical Programming, 138 (1), 115-139, 2013.
  68. G. Lan, “An optimal method for stochastic composite optimization”, submitted for publication, June 2008; Mathematical Programming, 133 (1), 365-397, 2012.
    • An initial version of the paper entitled “Efficient methods for stochastic composite optimization” was released in optimization online in June 2008, and won the INFORMS ICS student paper competition and the INFORMS George Nicholson Prize Competition second place in October, 2008.
  69. G. Lan, A. Nemirovski, and A. Shapiro, “Validation analysis of mirror descent stochastic approximation method”, submitted for publication, May 2008; Mathematical Programming, 134 (2), 425-458, 2012.
  70. A. Nemirovski, A.Juditsky, G. Lan, and A. Shapiro, “Robust stochastic approximation approach to stochastic programming“, submitted for publication, Sep. 2007; SIAM Journal on Optimization 19, 1574-1609, 2009.
  71. G. Lan, R.D.C. Monteiro, and T. Tsuchiya, “A polynomial predictor-corrector trust-region algorithm for linear programming”, submitted for publication, June 2007; SIAM Journal on Optimization 19, 1918-1946, 2009.
  72. G. Lan, Z. Lu, and R.D.C. Monteiro, “Primal-dual first-order methods with ${\cal O}(1/\epsilon)$ iteration complexity for cone programming”, submitted for publication, Dec. 2006; Mathematical Programming, 126, 1-29, 2011.
  73. G. Lan and G. W. DePuy, “On the effectiveness of incorporating randomness and memory into a multi-start metaheuristic with application to the Set Covering Problem“, submitted for publication, 2005; Computer & Industrial Engineering 51, 362-374, 2006.
  74. G. Lan, G. W. DePuy, and G. E. Whitehouse, “An effective and simple heuristic for the set covering problem”, submitted for publication, 2004; European Journal of Operational Research 176, 1387-1403, 2007.

Conference Papers

  1. Y. Li*, D. Choudhardy, X. Wei, B. Yuan, B. Bhushanam, T. Zhao and G. Lan,  Frequency-aware SGD for Efficient Embedding Learning with Provable Benefits, ICLR 2022.
  2. T. Xu*, Y. Liang and G. Lan, CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee, ICML 2021.
  3. D. Boob*, Q. Deng, G. Lan, and Y. Wang*, A feasible level proximal point method for nonconvex sparse constrained optimization, NeurIPS 2020.
  4. H. Shrivastava*, X. Chen*, B. Chen*, L. Lan, S. Alurru, H. Liu, and L. Song, GLAD: Learning sparse graph recovery, ICLR 2020.
  5. G. Lan, Z. Li* and Y. Zhou, A unified variance-reduced accelerated gradient method for convex optimization, NeurIPS 2019.
  6. Z. Wang*, Y. Zhou*, Y. Liang, and G. Lan, Cubic regularization with momentum for nonconvex optimization, UAI 2019.
  7. Z. Wang*, Y. Zhou*, Y. Liang, and G. Lan, “Sample Complexity of Stochastic Variance-Reduced Cubic Regularization for Nonconvex Optimization“, AISTATS 2018.
  8. D. Boob* and G. Lan, Theoretical properties of the global optimizer of two layer neural network, submitted for publication, October 2017.
  9. G. Lan, S. Pokutta, Y. Zhou* and D. Zink*, Conditional Accelerated Lazy Stochastic Gradient Descent,  ICML 2017.

Thesis