Generalized convexity: Their applications to multiobjective programming

Abstract

The aim of this paper is to show some applicable results to multiobjective optimization problems and the role that the Generalized Convexity plays in them. The study of convexity for sets and functions has special relevance in the search of optimal functions, and in the development of algorithms for solving optimization problems. However, the absence of convexity implies a total loss of effectiveness of the Optimization Theory methods, ie, the results are being verified under less stringent conditions, it was what became known as Generalized convexity. The literature generated around this topic has demonstrated its importance both from a theoretical point of view as practical, but it has also generated an enormous amount of papers with little scientific input.