Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 37 min ago
PreprintCC BY 4.0arXiv

A Safeguarded Projected-Gradient Framework for Complementarity Constrained Least Squares Problems

  • Lianghai Xiao
  • Wei Zhang
  • Jiayi Zhong
Open at sourcePDFDOICite

Abstract

Both generalized absolute value equations (GAVEs) and linear complementarity problems (LCPs) can be formulated as least-squares problems over the complementarity set. Because this feasible set is nonconvex, projected stationarity does not in general imply zero residual. We develop a safeguarded projected-gradient framework with a linear-system refinement on a selected polyhedral face. We establish matrix conditions under which every projected stationary point is a global solution and derive corresponding global convergence results. Specifically, when refinement on a correct active face returns a solution, we give explicit iteration bounds for active-face identification and prove finite termination. Numerical experiments on GAVE and LCP benchmarks demonstrate the high accuracy of the proposed framework across the tested settings.

Related

  1. A Safeguarded Transport-Extrapolated Proximal Gradient Method on the Stiefel Manifold
    Chuanjun Yan, Lin Chen
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref
  2. SAFEGUARDED NEURALLY-ACCELERATED PRECONDITIONING (SNAP) FRAMEWORK FOR NONLINEAR OPTIMIZATION
    Youngkyu Lee, George Em Karniadakis, Alena Kopaničáková
    HALPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingOptimisation & controlHALarXiv
  3. Broximal Gradient Descent: A Projection-Free Sister of Projected Gradient Descent
    Peter Richtárik, Kaja Gruntkowska, Hanmin Li
    arXivPreprintCC0Full textOptimisation & controlStatisticsarXiv
  4. The Projected Hessian Quantification Theorem: Exact Duality For Constrained Eigenvalues
    Meiling Wang, Yong Xia
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  5. An Adaptive Projected-Gradient Algorithm for Sample-Average Approximations of Stochastic Multi-Objective Optimization
    Yiyang Li, Lei Wang, Xiaojun Chen
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{xiao2026safeguarded,
  title = {{A Safeguarded Projected-Gradient Framework for Complementarity Constrained Least Squares Problems}},
  author = {Lianghai Xiao and Wei Zhang and Jiayi Zhong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.20786},
  eprint = {2607.20786},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.20786},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Safeguarded Projected-Gradient Framework for Complementarity Constrained Least Squares Problems
AU  - Lianghai Xiao
AU  - Wei Zhang
AU  - Jiayi Zhong
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2607.20786
UR  - https://arxiv.org/abs/2607.20786
AB  - Both generalized absolute value equations (GAVEs) and linear complementarity problems (LCPs) can be formulated as least-squares problems over the complementarity set. Because this feasible set is nonconvex, projected stationarity does not in general imply zero residual. We develop a safeguarded projected-gradient framework with a linear-system refinement on a selected polyhedral face. We establish matrix conditions under which every projected stationary point is a global solution and derive corresponding global convergence results. Specifically, when refinement on a correct active face returns a solution, we give explicit iteration bounds for active-face identification and prove finite termination. Numerical experiments on GAVE and LCP benchmarks demonstrate the high accuracy of the proposed framework across the tested settings.
ER  -