Tightening a copositive relaxation for standard quadratic optimization problems

Yong Xia, Ruey Lin Sheu, Xiaoling Sun, Duan Li

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

摘要

We focus in this paper the problem of improving the semidefinite programming (SDP) relaxations for the standard quadratic optimization problem (standard QP in short) that concerns with minimizing a quadratic form over a simplex. We first analyze the duality gap between the standard QP and one of its SDP relaxations known as "strengthened Shor's relaxation". To estimate the duality gap, we utilize the duality information of the SDP relaxation to construct a graph G * . The estimation can be then reduced to a two-phase problem of enumerating first all the minimal vertex covers of G * and solving next a family of second-order cone programming problems. When there is a nonzero duality gap, this duality gap estimation can lead to a strictly tighter lower bound than the strengthened Shor's SDP bound. With the duality gap estimation improving scheme, we develop further a heuristic algorithm for obtaining a good approximate solution for standard QP.

原文English
頁(從 - 到)379-398
頁數20
期刊Computational Optimization and Applications
55
發行號2
DOIs
出版狀態Published - 2013 六月

All Science Journal Classification (ASJC) codes

  • 控制和優化
  • 計算數學
  • 應用數學

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