Generalized Stationary Points and an Interior Point Method for MPEC

Mathematical program with equilibrium constraints (MPEC)has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC.A primal-dual interior point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or linear independence constraint qualification. Under very general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limiting point of the generated sequence is a piece-wise stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are satisfactory, which include a case analyzed by Leyffer for which the penalty interior point algorithm failed to find a stationary solution.Singapore-MIT Alliance (SMA

Strong stationary solutions to equilibrium problems with equilibrium constraints with applications to an electricity spot market model

In this paper, we consider the characterization of strong stationary solutions to equilibrium problems with equilibrium constraints (EPECs). Assuming that the underlying generalized equation satisfies strong regularity in the sense of Robinson, an explicit multiplier-based stationarity condition can be derived. This is applied then to an equilibrium model arising from ISO-regulated electricity spot markets

Construção e analise de um algoritmo PQS globalmente convergente

Orientador: Sandra Augusta SantosDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Os métodos de programação quadrática seqüencial (PQS) são as generalizações do método de Newton para o problema geral de otimização com restrições. Neste trabalho, um algoritmo baseado no método PQS para resolver o problema geral de programação não linear na forma padrão é analisado. A função de mérito utilizada é do tipo Lagrangeano aumentado com uma atualização não-monótona para a seqüência dos parâmetros de penalidade. Apresentamos as demonstrações dos resultados de boa definição e convergência global. Introduzimos uma estratégia para lidar com os subproblemas quadráticos baseado na minimização em caixas. Duas escolhas para a matriz Hessiana do modelo quadrático são sugeridas. Um levantamento bibliográfico recente compõe a Introdução. Palavras-chave: Algoritmo PQS; boa definição, convergência global; subproblemas quadráticos; Lagrangeano aumentado; minimização em caixas.Abstract: Not informed.MestradoMestre em Matemática Aplicad

Some Feasibility Issues in Mathematical Programs with Equilibrium Constraints

This paper is concerned with some feasibility issues in mathematical programs with equilibrium constraints (MPECs) where additional joint constraints are present that must be satisfied by the state and design variables of the problems. We introduce sufficient conditions that guarantee the feasibility of these MPECs. It turns out that these conditions also guarantee the feasibility of the quadratic programming subproblems arising from the penalty interior point algorithm (PIPA) and the sequential quadratic programming (SQP) algorithm for solving MPECs; thus the same conditions ensure that these algorithms are applicable for solving this class of jointly constrained MPECs