Análisis y resolución numérica de problemas de programación matemática con restricciones de equilibrio y complementariedad (MPECs) : resolución de MPCCs y MPECs clásicos con métodos de tipo Semismooth Newton (SSN).

Abstract

This paper deals with the study of mathematical programming problems with complementarity constraints MPCC by means of a reformulation based on the lifting technique. Then, we study the Lagrangian optimality system that characterizes the stationary points of the reformulated problem with the help of a suitable function. Subsequently, a Semi-Smooth Newton (SSN) type algorithm is constructed (in the first instance, with a local scope and subsequently globali zation is achieved), which possesses a special focus on the B-subdifferentials and the properties that allow a correct incorporation of second order information into the Newton type system matrix, constructed from the mentioned subdifferentials. With this, the superlinear convergence of the method can be guaranteed. Finally, we perform the implementation of the algorithm in MATLAB language and examples are proposed to evaluate the performance of the code.