A penalty method and a regularization strategy to solve MPCC. (English) Zbl 1211.65075
Summary: The goal of this paper is to solve mathematical programs with complementarity constraints (MPCC) using nonlinear programming techniques. This work presents two algorithms based on several nonlinear techniques such as sequential quadratic programming, penalty techniques and regularization schemes. A set of modeling language for mathematical programming problems is tested and the computational experience shows that both algorithms are effective.
MSC:
65K05 | Numerical mathematical programming methods |
90C30 | Nonlinear programming |
90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
90C55 | Methods of successive quadratic programming type |
Keywords:
numerical examples; mathematical programs with complementarity constraints; nonlinear programming; algorithms; sequential quadratic programming; penalty techniques; regularization schemesSoftware:
AMPLReferences:
[1] | Anitescu M., SIAM J. Optim. 15 pp 1203– (2005) · Zbl 1097.90050 · doi:10.1137/S1052623402401221 |
[2] | Bertsekas D., Nonlinear Programming (1995) |
[3] | Dolan E. D., Math. Program. A 91 pp 201– (2001) · Zbl 1049.90004 · doi:10.1007/s101070100263 |
[4] | Fletcher, R., Leyffer, S., Ralph, D. and Scholtes, S. 2002. ”Local convergence of SQP methods for mathematical programs with equilibrium constraints”. Tech. Rep., Numerical Analysis Report NA/209, Department of Mathematics, University of Dundee · Zbl 1112.90098 |
[5] | Fourer R., AMPL: A Modelling Language for Mathematical Programming (1993) |
[6] | Fukushima M., Lecture Notes Econom. Math. Systems 447 pp 99– (1999) |
[7] | S. Leyffer, MacMPEC. Available athttp://wiki.mcs.anl.gov/leyffer/index.php/MacMPEC, 2000 |
[8] | Ralph D., Optim. Methods Softw. 19 pp 527– (2004) · Zbl 1097.90054 · doi:10.1080/10556780410001709439 |
[9] | Scheel H., Math. Oper. Res. 25 pp 1– (2000) · Zbl 1073.90557 · doi:10.1287/moor.25.1.1.15213 |
[10] | Scholtes S., SIAM J. Optim. 11 pp 918– (2001) · Zbl 1010.90086 · doi:10.1137/S1052623499361233 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.