Nonconvex functions and variational inequalities

作     者：Noor, MA 

作者机构：Department of Mathematics College of Science King Saud University Riyadh Saudi Arabia 

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

年 卷 期：1995年第87卷第3期

页      面：615-630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：nonconvex functions semipreinvex functions semi-invex sets variational-like inequalities iterative algorithms 

摘      要：In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and are-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm.