Análisis y resolución numérica de problemas de programación matemática con restricciones de equilibrio y complementariedad : resolución de mpccs clásicos con métodos de tipo sqp (sequential quadratic programming).

Abstract

This document contains a theoretical study of the lifting technique for the formulation of mathematical problems with complementary constraints (MPCCs). Also, it describes the mathematical underpinning required in the construction of a nonsmooth SQP algorithm used for a numerical resolution of these problems. This algorithm uses the above mentioned technique with a special focus on B-subdifferentials and the properties that allow a correct choice of the positive definite matrix necessary to guarantee the convergence of the algorithm. The operation of the semismooth SQP method is described and how it takes advantage of applying lifting to MPCC to construct suitable subproblems at each iteration of the proposed algorithm. Finally, a proposed implementation of this algorithm in the Python programming language is presented and some numeric examples are given.