Publications

Preprints

• Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds
  Alex L. Wang
  December 2025 [arXiv]

• Subgame Perfect Methods in Nonsmooth Convex Optimization
  (ɑ) Benjamin Grimmer and Alex L. Wang
  November 2025 [arXiv]

• Beyond Minimax Optimality: A Subgame Perfect Gradient Method
  (ɑ) Benjamin Grimmer, Kevin Shu, and Alex L. Wang
  December 2024 [arXiv][code]

• Sharpness and well-conditioning of nonsmooth convex formulations in statistical signal recovery
  (ɑ) Lijun Ding and Alex L. Wang
  July 2023 [arXiv] [code]

Journal publications

• Composing optimized stepsize schedules for gradient descent
  (ɑ) Benjamin Grimmer, Kevin Shu, and Alex L. Wang
  Math. Oper. Res. 2025 [arXiv][code]

• Accelerated Objective Gap and Gradient Norm Convergence for Gradient Descent via Long Steps
  (ɑ) Benjamin Grimmer, Kevin Shu, and Alex L. Wang
  INFORMS J. Optim. 2025
  [arXiv] [article] [mathematica]
  • This paper significantly shortens and strengthens the analysis for the stepsize sequences first described in our previous technical report Accelerated Gradient Descent via Long Steps.

• New notions of simultaneous diagonalizability of quadratic forms with applications to QCQPs
  Alex L. Wang and Rujun Jiang
  Math. Program. 2024 [arXiv] [article]

• Hidden convexity, optimization, and algorithms on rotation matrices
  (ɑ) Akshay Ramachandran, Kevin Shu, and Alex L. Wang
  Math. Oper. Res. 2024 [arXiv] [article]

• Accelerated first-order methods for a class of semidefinite programs
  Alex L. Wang and Fatma Kılınç-Karzan
  Math. Program. 2024 [arXiv] [article] [code]

• On semidefinite descriptions for convex hulls of quadratic programs
  Alex L. Wang and Fatma Kılınç-Karzan
  Oper. Res. Letters (2024) [arXiv] [article]
  • This paper was significantly condensed and rewritten during the review process. The original manuscript, A Geometric View of SDP Exactness in QCQPs and its Applications [arXiv], contains additional minor results on exactness in random QCQPs.

• Implicit regularity and linear convergence rates for the generalized trust-region subproblem
  Alex L. Wang, Yunlei Lu, and Fatma Kılınç-Karzan
  SIAM J. Optim. (2023) [arXiv] [article]

• Necessary and sufficient conditions for rank-one generated cones
  (ɑ) C.J. Argue, Fatma Kılınç-Karzan, and Alex L. Wang
  Math. Oper. Res. (2022)
  [arXiv] [article]

• Exactness in SDP relaxations of QCQPs: Theory and applications
  (ɑ) Fatma Kılınç-Karzan and Alex L. Wang
  Tut. in Oper. Res. (2021) [arXiv] [article]

• On the tightness of SDP relaxations of QCQPs
  Alex L. Wang and Fatma Kılınç-Karzan
  Math. Program. (2022) [arXiv] [article]
  INFORMS Optimization Society 2021 Student Paper Prize

• The generalized trust region subproblem: solution complexity and convex hull results
  Alex L. Wang and Fatma Kılınç-Karzan
  Math. Program. (2022) [arXiv] [article]

Articles in refereed conference proceedings

• Solving Stackelberg Prediction Game with Least Squares Loss via Spherically Constrained Least Squares Reformulation
  Jiali Wang, Wen Huang, Rujun Jiang, Xudong Li, and Alex L. Wang
  ICML 2022 [arXiv] [proceedings]
  ICML 2022 Outstanding Paper Award

• On convex hulls of epigraphs of QCQPs
  Alex L. Wang and Fatma Kılınç-Karzan
  IPCO 2020 [arXiv] [proceedings]

• Hardy-Muckenhoupt bounds for Laplacian eigenvalues
  (ɑ) Gary Miller, Noel Walkington, and Alex L. Wang
  APPROX 2019 [arXiv] [proceedings]

• Clustering stable instances of Euclidean k-means
  (ɑ) Abhratanu Dutta, Aravindan Vijayaraghavan, and Alex L. Wang
  NeurIPS 2017 [arXiv] [proceedings]

Other writing

• A Strengthened Conjecture on the Minimax Optimal Constant Stepsize for Gradient Descent
  (ɑ) Benjamin Grimmer, Kevin Shu, and Alex L. Wang
  July 2024 [arXiv] [certificates]
  • This paper makes partial progress towards a conjecture on the minimax optimal constant stepsize for gradient descent. This conjecture was resolved shortly after this paper was posted online.

• On QCQPs and their SDP Relaxations — Ph.D. Thesis
  June 2022 [CMU CSD]

• Weighted Cheeger and Buser inequalities, with applications to clustering and cutting probability densities
  (ɑ) Timothy Chu, Gary Miller, Noel Walkington, and Alex L. Wang
  May 2020 [arXiv]