On the Second Order Optimality Conditions for Optimization Problems with Inequality Constraints

作     者：Mourad Naffouti 

作者机构：Department of Mathematics Faculty of Science Mathematics Physics and Natural of Tunis Tunis Tunisia 

出 版 物：《Open Journal of Optimization》 (最优化（英文）)

年 卷 期：2013年第2卷第4期

页      面：109-115页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

主　　题：Optimality Conditions Constraint Qualifications Copositivity 

摘      要：A nonlinear optimization problem (P) with inequality constraints can be converted into a new optimization problem (PE) with equality constraints only. This is a Valentine method for finite dimensional optimization. We review second order optimality conditions for (PE) in connection with those of (P). A strictly complementary slackness condition can be made to get the property that sufficient optimality conditions for (P) imply the same property for (PE). We give some new results (see Theorems 3.1, 3.2 and 3.3) .Without any assumption, a counterexample is given to show that these conditions are not equivalent.