Vector optimization is continuously needed in several science fields, particularly in economy and engineering. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming.
The search for solutions to vector or multiobjective mathematical programming problems has been carried out through the study of optimality conditions and of the properties of the functions that are involved, as well as through the study of the respective dual problems. In the case of optimality conditions, it is customary to use critical points of the Kuhn-Tucker or Fritz John type. In the case of the classes of functions employed in mathematical programming problems, the tendency has been to substitute convex functions with more general ones, with the objective of obtaining a solution through an optimality condition. Meanwhile the inverse result has also been sought. At the same time, optimality conditions, vector functions and optimality results are being generalized from the differentiable case to the non-differentiable one, and otherwise, extended to other kind of problems, such as continuous time problems.
The aim of this book is to present the last developments in vector optimization. We deeply appreciate the contribution of many of the most relevant researchers in the area that have made possible the existence of this book.
Manuel Arana Jiménez
Gabriel Ruiz Garzón
Antonio Rufián Lizana