arXiv subjects

Yingxin Zhou

Publications and source records attributed to Yingxin Zhou.

3 recordsLinked to original sources

arXiv2026

A Barrier Primal Dual Hybrid Gradient Method for Solving Linear Programming Problems

Primal Dual Hybrid Gradient (PDHG) method has been verified to exhibit a two stage convergence behavior, in which a prolonged active set identification phase may be a major issue of slow convergence. In this paper, we propose Barrier PDHG (BPDHG), a nested algorithm which incorporates a logarithmic barrier function into the PDHG framework to alleviate this problem. We first establish convergence of the inner iterations, derive an error bound for the corresponding inner problem. Then we prove that the outer sequence generated by BPDHG approaches the optimal solution set of the LP problem we considered. Furthermore, we integrate the barrier technique into the {Primal Dual Linear Programming} (PDLP) framework to develop the corresponding Barrier PDLP (BPDLP) method. Numerical experiments show that the barrier modification can alleviate prolonged plateaus in the KKT residual on selected instances. We also investigate an empirical instance-dependent indicator for identifying LP problems on which BPDLP is more likely to outperform PDLP.

math.OC↗

arXiv2025

Anderson Accelerated Primal-Dual Hybrid Gradient for solving LP

We present the Anderson Accelerated Primal--Dual Hybrid Gradient (AA-PDHG), a fixed-point-based framework that integrates Anderson Acceleration into the PDHG method for solving linear programming (LP) problems. A central motivation is to investigate whether Anderson Acceleration, which systematically exploits multi-step historical information, can serve as a viable alternative to the restart strategy for PDHG. We establish the global convergence of AA-PDHG under a safeguard condition and propose a filtered variant (FAA-PDHG) that enforces the uniform boundedness of the coefficient matrix through angle and length filtering, thereby providing a rigorous convergence guarantee. Numerical experiments on LP instances derived from MIPLIB 2017 demonstrate that both AA-PDHG and FAA-PDHG deliver significant speedups over vanilla PDHG. On pre-solved MIPLIB instances, AA-PDHG is the fastest method on about 70% of the benchmark when neither method uses primal-weight updates, and remains competitive when both AA-PDHG and restart PDHG use their respective primal-weight update strategies, establishing Anderson Acceleration as a competitive alternative to the restart mechanism.

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arXiv2024

An Inertial Bregman Proximal DC Algorithm for Generalized DC Programming with Application to Data Completion

In this paper, we consider a class of generalized difference-of-convex functions (DC) programming, whose objective is the difference of two convex (not necessarily smooth) functions plus a decomposable (possibly nonconvex) function with Lipschitz gradient. By employing the Fenchel-Young inequality and Moreau decomposition theorem, we introduce an inertial Bregman proximal DC algorithm to solve the problem under consideration. Our algorithmic framework is able to fully exploit the decomposable structure of the generalized DC programming such that each subproblem of the algorithm is enough easy in many cases. Theoretically, we show that the sequence generated by the proposed algorithm globally converges to a critical point under the Kurdyka-Łojasiewicz condition. A series of numerical results demonstrate that our algorithm runs efficiently on matrix and tensor completion problems.

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