Generalized separation theorems and the Farkas’ lemma

AbstractThe main purpose of this paper is to extend the conventional separation theorems concerning the convex subset of Rm to generalized separation theorems concerning the convex subset of Rm×Sn. This is accomplished by the introduction of the generalized inner product in Rm×Sn. Then we derive the famous Farkas’ lemma in nonlinear semidefinite programming, which may be very important for the analysis of the dual theory and optimality conditions of nonlinear semidefinite programming

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics