The eigenvalue complementarity problem

Abstract In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation–Linearization Technique (Rlt)-based tree search algorithm is introduced for processing the EiCP via the lattermost of these formulations. Computational experience is included to highlight the efficacy of the above formulations and corresponding techniques for the solution of the EiCP.

[1]  S. Dirkse,et al.  The path solver: a nommonotone stabilization scheme for mixed complementarity problems , 1995 .

[2]  Richard W. Cottle,et al.  Linear Complementarity Problem , 2009, Encyclopedia of Optimization.

[3]  Hanif D. Sherali,et al.  Complementarity Active-Set Algorithm for Mathematical Programming Problems with Equilibrium Constraints , 2007 .

[4]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[5]  Joaquim J. Júdice,et al.  On the solution of NP-hard linear complementarity problems , 2002 .

[6]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[7]  J. Júdice,et al.  Solution of a General Linear Complementarity Problem Using Smooth Optimization and Its Application to Bilinear Programming and LCP , 2001 .

[8]  Joaquim Júdice,et al.  A sequential LCP method for bilevel linear programming , 1992, Ann. Oper. Res..

[9]  Joaquim Júdice,et al.  The symmetric eigenvalue complementarity problem , 2003, Math. Comput..

[10]  Jonathan F. Bard,et al.  A Branch and Bound Algorithm for the Bilevel Programming Problem , 1990, SIAM J. Sci. Comput..

[11]  Joaquim J. Júdice,et al.  The directional instability problem in systems with frictional contacts , 2004 .

[12]  Michael A. Saunders,et al.  MINOS 5. 0 user's guide , 1983 .

[13]  Hanif D. Sherali,et al.  A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique , 1992, J. Glob. Optim..

[14]  Hanif D. Sherali,et al.  On the asymmetric eigenvalue complementarity problem , 2009, Optim. Methods Softw..

[15]  S. J. Chung.  NP-Completeness of the linear complementarity problem , 1989 .

[16]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[17]  Hanif D. Sherali,et al.  A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints , 2006, J. Glob. Optim..

[18]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .