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<p>This paper proposes an output space branch-and-bound algorithm for solving the sum of convex quadratic-over-linear fractions problem. Firstly, the original problem is equivalently transformed into a linear fractional programming problem (SDFP1) on the cone of positive semidefinite matrices based on semidefinite programming theory, where the non-convexity of SDFP1 arises from the non-convexity of its objective function. Leveraging the analytical properties of the objective function in SDFP1, a semidefinite relaxation programming problem is constructed for SDFP1. By integrating the branch-and-bound framework with the obtained theoretical results, a novel output space branch-and-bound algorithm is devised, with its convergence and complexity demonstrated in the paper. Numerical experiments illustrate the feasibility and effectiveness of the proposed algorithm.</p>

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An Output Space Branch-and-Bound Algorithm for Solving the Sum of Convex Quadratic-over-Linear Fractions Problem

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Xiao-Li Huang,
  • Yue-Lin Gao,
  • Xiao-Hua Ma,
  • Xia Liu

摘要

This paper proposes an output space branch-and-bound algorithm for solving the sum of convex quadratic-over-linear fractions problem. Firstly, the original problem is equivalently transformed into a linear fractional programming problem (SDFP1) on the cone of positive semidefinite matrices based on semidefinite programming theory, where the non-convexity of SDFP1 arises from the non-convexity of its objective function. Leveraging the analytical properties of the objective function in SDFP1, a semidefinite relaxation programming problem is constructed for SDFP1. By integrating the branch-and-bound framework with the obtained theoretical results, a novel output space branch-and-bound algorithm is devised, with its convergence and complexity demonstrated in the paper. Numerical experiments illustrate the feasibility and effectiveness of the proposed algorithm.