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arXiv · 2607.20786

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

Lianghai Xiao·Wei Zhang·Jiayi Zhong
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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.

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Lianghai Xiao, Wei Zhang, Jiayi Zhong. 2026-07-22. A Safeguarded Projected-Gradient Framework for Complementarity Constrained Least Squares Problems. https://arxiv.org/abs/2607.20786

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