Deduction of a new algorithm for solving constrained optimization problems Deducción de un nuevo algoritmo para la resolución de problemas de optimización con restricciones

Abstract

With the aim of providing a new vision in solving some optimization problems, this articlewill deal with the deduction of a new numerical method in optimization. To do this, a generic mo-deling of the problems to be solved will be proposed. In this way, the necessary preliminaries will beintroduced to be able to proceed with the deduction that will be made later. In this sense, the proposedmethod will be framed within the feasible directions methods, for which simple topological concepts(related to the admissible set) and definitions related to the feasible and descent directions that maybe considered will be introduced. Subsequently, we will proceed with the deduction of the algorithmpresented in this article, ensuring that the reader can observe the procedure for its construction. Inaddition, the computational aspects of the method will be introduced and a series of codes will beproposed that will allow the algorithm to be implemented in a programming language. In the caseof this article, MatLab will be used. Finally, the results obtained when executing the method will be shown together with other methods already known to be able to compare the results obtained. In thisway, it will be concluded by providing the most relevant conclusions and future lines of research toimprove the presented method.