Scholarlink

<p>This paper investigates a Stage-wise Homotopy Alternating Direction Method of Multipliers (Stage-wise HADMM) for the nonconvex quadratic programming problem. The method integrates a homotopy map into the ADMM framework, solving the original nonconvex problem by tracing a solution path through a series of progressively deformed subproblems. We design a “double-loop” framework: the outer loop advances the problem’s nonconvexity along a predefined homotopy path, while the inner loop employs proximal ADMM iterations to stabilize the solution at each stage. This “stabilize first, then advance” strategy effectively guides the algorithm to avoid poor local minima. We theoretically prove that the entire iteration sequence globally converges to a KKT point of the Moreau–Yosida regularized reformulation. Numerical experiments validate the robustness of the algorithm, specifically, we analyze the impact of the geometric shape of the homotopy sequence and find that aggressive “relaxation-type” sequences yield the highest computational efficiency. Furthermore, in real-world portfolio optimization backtests using S&amp;P 500 data, the proposed method outperforms representative nonconvex solvers (DCA, ProxADMM) in terms of net wealth accumulation. Compared to standard convex regularization pipelines (SCAD, Ledoit–Wolf), our approach shows greater resilience to transaction costs by reducing portfolio turnover.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A stage-wise homotopy ADMM for solving nonconvex quadratic programming problem

  • 期刊论文

  • 发表日期：

    2026年3月30日

查看全文
  • Xianghui Huang,
  • Zhensheng Yu

摘要

This paper investigates a Stage-wise Homotopy Alternating Direction Method of Multipliers (Stage-wise HADMM) for the nonconvex quadratic programming problem. The method integrates a homotopy map into the ADMM framework, solving the original nonconvex problem by tracing a solution path through a series of progressively deformed subproblems. We design a “double-loop” framework: the outer loop advances the problem’s nonconvexity along a predefined homotopy path, while the inner loop employs proximal ADMM iterations to stabilize the solution at each stage. This “stabilize first, then advance” strategy effectively guides the algorithm to avoid poor local minima. We theoretically prove that the entire iteration sequence globally converges to a KKT point of the Moreau–Yosida regularized reformulation. Numerical experiments validate the robustness of the algorithm, specifically, we analyze the impact of the geometric shape of the homotopy sequence and find that aggressive “relaxation-type” sequences yield the highest computational efficiency. Furthermore, in real-world portfolio optimization backtests using S&P 500 data, the proposed method outperforms representative nonconvex solvers (DCA, ProxADMM) in terms of net wealth accumulation. Compared to standard convex regularization pipelines (SCAD, Ledoit–Wolf), our approach shows greater resilience to transaction costs by reducing portfolio turnover.