Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere

Van Bong Nguyen, Thi Ngan Nguyen, Ruey Lin Sheu

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this paper, we study the strong duality for an optimization problem to minimize a homogeneous quadratic function subject to two homogeneous quadratic constraints over the unit sphere, called Problem (P) in this paper. When a feasible (P) fails to have a Slater point, we show that (P) always adopts the strong duality. When (P) has a Slater point, we propose a set of conditions, called “Property J”, on an SDP relaxation of (P) and its conical dual. We show that (P) has the strong duality if and only if there exists at least one optimal solution to the SDP relaxation of (P) which fails Property J. Our techniques are based on various extensions of S-lemma as well as the matrix rank-one decomposition procedure introduced by Ai and Zhang. Many nontrivial examples are constructed to help understand the mechanism.

原文English
頁(從 - 到)121-135
頁數15
期刊Journal of Global Optimization
76
發行號1
DOIs
出版狀態Published - 2020 1月 1

All Science Journal Classification (ASJC) codes

  • 電腦科學應用
  • 管理科學與經營研究
  • 控制和優化
  • 應用數學

指紋

深入研究「Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere」主題。共同形成了獨特的指紋。

引用此