Publications

Preprints

• Accelerated Objective Gap and Gradient Norm Convergence for Gradient Descent via Long Steps
  (ɑ) Benjamin Grimmer, Kevin Shu, and Alex L. Wang
  March 2024
  [arXiv] [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.

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

• New notions of simultaneous diagonalizability of quadratic forms with applications to QCQPs
  Alex L. Wang and Rujun Jiang
  January 2021
  [arXiv]

Journal publications

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

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

• On semidefinite descriptions for convex hulls of quadratic programs
  Alex L. Wang and Fatma Kılınç-Karzan
  Oper. Res. Letters, Online first (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., 33 (2), 1250-1278, (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., 48(1):100-126, (2022)
  [arXiv] [article]

• Exactness in SDP relaxations of QCQPs: Theory and applications
  (ɑ) Fatma Kılınç-Karzan and Alex L. Wang
  Tut. in Oper. Res., 312-345 (2021)
  [arXiv] [article]

• On the tightness of SDP relaxations of QCQPs
  Alex L. Wang and Fatma Kılınç-Karzan
  Math. Program., 193, 33–73 (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., 191, 445–486 (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 (Int. Conf. Mach. Learn.)
  [arXiv] [proceedings]
  ICML 2022 Outstanding Paper Award

• On convex hulls of epigraphs of QCQPs
  Alex L. Wang and Fatma Kılınç-Karzan
  IPCO 2020 (Integer Programming and Comb. Optim.)
  [arXiv] [proceedings]

• Hardy-Muckenhoupt bounds for Laplacian eigenvalues
  (ɑ) Gary Miller, Noel Walkington, and Alex L. Wang
  APPROX 2019 (Int. Workshop on Approx. Algorithms for Comb. Optim. Prob.)
  [arXiv] [proceedings]

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

Other writing

• Accelerated Gradient Descent via Long Steps
  (ɑ) Benjamin Grimmer, Kevin Shu, and Alex L. Wang
  September 2023
  [arXiv] [mathematica proofs]

• 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]