A Note on Legendre–Fenchel Conjugate of the Product of Two Positive-Definite Quadratic Forms  

作　　者：Yong Xia 

机构地区：[1]State Key Laboratory of Software Development Environment,Key Laboratory of Mathematics,Informatics and Behavioral Semantics of the Ministry of Education,School of Mathematics and System Sciences,Beihang University,Beijing 100191,P.R.China

出　　处：《Journal of the Operations Research Society of China》2013年第3期333-338,共6页中国运筹学会会刊（英文）

基　　金：This research was supported by National Natural Science Foundation of China(Nos.11001006 and 91130019/A011702);by the Fundamental Research Funds for the Central Universities(No.YWF-13-A01);d by the Fund of State Key Laboratory of Software Development Environment(No.SKLSDE-2013ZX-13);The author is grateful to the two anonymous referees whose comments improved this paper.The author also thanks Prof.Yun-Bin Zhao,Prof.Henry Wolkowicz and his doctoral student Minghua Lin for valuable comments.

摘　　要：The Legendre–Fenchel conjugate of the product of two positive-definite quadratic forms was posted as an open question in the field of nonlinear analysis and optimization by Hiriart-Urruty[‘Question 11’in SIAM Review 49,255–273,2007].Under a convexity assumption on the function,it was answered by Zhao[SIAM J.Matrix Analysis&Applications 31(4),1792–1811,2010].In this note,we answer the open question without making the convexity assumption.

关 键 词：Legendre-Fenchel conjugate Quadratic form 

分 类 号：O17[理学—数学]