关于二次方程程凸壳的半无限描述

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-03-07 DOI:10.1016/j.orl.2024.107108

Alex L. Wang , Fatma Kılınç-Karzan

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引用次数: 0

摘要

二次受限程序（QCQPs）是一类极富表现力的非凸优化问题。虽然 QCQPs 在一般情况下是 NP-困难的，但它们可以通过标准半定量程序（SDP）松弛进行自然的凸松弛。在本文中，我们研究了 QCQP 上图的凸壳何时与 SDP 松弛的投影上图重合。我们提出了凸壳精确性的充分条件，并证明在额外的几何假设下，该条件是进一步必要的。这个充分条件是基于Γ、凸拉格朗日乘数锥及其近亲Γ1 和Γ∘的几何性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On semidefinite descriptions for convex hulls of quadratic programs

Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP) relaxation. In this paper we study when the convex hull of the epigraph of a QCQP coincides with the projected epigraph of the SDP relaxation. We present a sufficient condition for convex hull exactness and show that this condition is further necessary under an additional geometric assumption. The sufficient condition is based on geometric properties of Γ, the cone of convex Lagrange multipliers, and its relatives $Γ_{1}$ and $Γ^{\circ}$ .

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.