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Nonlinear Systems Optimization and Statistics group

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MPCC - Mathematical Program with Complementarity Constraints

NLP solvers have been used to solve a range of MPCC, in particular, SQP methods have been very successful. Based on SQP technique, the idea is to expand the filter method to the MPCC context, implementing a filter with three components to be able to consider the complementarity violation. Approaches like regularization schemes and penalty functions have been implemented and the preliminary numerical results seem very promising. A theoretical study must be provided. This analysis will be applied to SIP. Identifying real problems that can be formulated as MPCC and making their mathematical model available to the scientific community for software testing purposes is another future challenge.

Research Team

M. Teresa T. Monteiro
A. Ismael F. Vaz

Publications

Antunes, A.M.S.; Monteiro, M.T.T., A SQP-filter algorithm with line search in nonlinear programming, XXVIII Congreso de Estadística e Investigación Operativa , ISBN: 84-689-0438-4 CD-ROM (9 pp), Cádiz, 2004.

Rodrigues, H.S.F; Monteiro, M.T.T., Mathematical Program with Complementarity Constraints as Nonlinear Program, XXVIII Congreso de Estadística e Investigación Operativa , ISBN: 84-689-0438-4 CD-ROM (11 pp), Cádiz, 2004.

Antunes, A.M.S.; Monteiro, M.T.T., A Filter Algorithm and other NLP Solvers: Performance Comparative Analysis. Lecture Notes in Economics and Mathematical Systems , Springer-Verlag, V. 563, 425-434, 2006 (in ISI since 2006).

Rodrigues, H.S.F; Monteiro, M.T.T., Solving Mathematical Programs with Complementarity Constraints with Nonlinear Solvers. Lecture Notes in Economics and Mathematical Systems , Springer-Verlag, V. 563, 415-424, 2006 (in ISI since 2006).

Rodrigues, H.S.F.; Monteiro, M.T.T.; Vaz, A.I.F., Mercado de Energia Eléctrica: uma modelação MPCC-NLP, Engenharia ’07 inovação & desenvolvimento , 6 pp, Covilhã, 2007.

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Poster