论文标题
惩罚二次约束二次优化的惩罚半决赛编程
Penalized Semidefinite Programming for Quadratically-Constrained Quadratic Optimization
论文作者
论文摘要
在本文中，我们提供了一种新的受惩罚的半决赛编程方法，用于非凸二次限制的二次程序（QCQPS）。我们将罚款项纳入凸松弛的目标，以便检索非凸QCQP的可行和近乎最佳的解决方案。我们引入了广义的线性独立约束资格（GLICQ）标准，并证明任何足够接近可行集合的GLICQ常规点都可以用于构建适当的罚款项并恢复可行的解决方案。受这些结果的启发，我们开发了一个启发式顺序程序，该程序可保留可行性，并旨在提高每次迭代的客观价值。关于大规模系统识别问题的数值实验以及二次编程库（QPLIB）的基准实例证明了拟议的惩罚性半决赛计划在寻找非convex qCQP的近乎最佳解决方案方面的能力。
In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve feasible and near-optimal solutions for non-convex QCQPs. We introduce a generalized linear independence constraint qualification (GLICQ) criterion and prove that any GLICQ regular point that is sufficiently close to the feasible set can be used to construct an appropriate penalty term and recover a feasible solution. Inspired by these results, we develop a heuristic sequential procedure that preserves feasibility and aims to improve the objective value at each iteration. Numerical experiments on large-scale system identification problems as well as benchmark instances from the library of quadratic programming (QPLIB) demonstrate the ability of the proposed penalized semidefinite programs in finding near-optimal solutions for non-convex QCQP.
