Mathematical properties of optimization problems defined by positively homogeneous functions

作     者：Lasserre, JB Hiriart-Urruty, JB 

作者机构：CNRS LAAS F-31077 Toulouse France Univ Toulouse 3 Dept Math F-31062 Toulouse France 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：2002年第112卷第1期

页      面：31-52页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：nonlinear programming homogeneous programming global optimization 

摘      要：We consider the nonlinear programming problem (sic)--{min f(x)\g(i)(x)less than or equal tob(i), i-1,...,m} with f positively p-homogeneous and g(i) positively q-homogeneous functions. We show that (sic) admits a simple min-max formulation (sic) with the inner max-problem being a trivial linear program with a single constraint. This provides a new formulation of the linear programming problem and the linear-quadratic one as well. In particular, under some conditions, a global (nonconvex) optimization problem with quadratic data is shown to be equivalent to a convex minimization problem.