On the asymmetric eigenvalue complementarity problem

Authors:
Joaquim J. Judice;Hanif D. Sherali;Isabel M. Ribeiro;Silverio S. Rosa
Affiliations:
Departamento de Matematica da Universidade de Coimbra and Instituto de Telecomunicacoes, Coimbra, Portugal;Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA;Seccao de Matematica do Departamento de Engenharia Civil, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal;Departamento de Matematica da Universidade da Beira Interior, Covilha, Portugal
Venue:
Optimization Methods & Software - GLOBAL OPTIMIZATION
Year:
2009

Citing 15
Cited 6

An experimental investigation of enumerative methods for the linear complementarity problem

Computers and Operations Research
New branch-and-bound rules for linear bilevel programming

SIAM Journal on Scientific and Statistical Computing
A sequential LCP method for bilevel linear programming

Annals of Operations Research - Special issue on hierarchical optimization
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
A Globally Convergent Sequential Quadratic Programming Algorithm for Mathematical Programs with Linear Complementarity Constraints

Computational Optimization and Applications
An Implementable Active-Set Algorithm for Computing a B-Stationary Point of a Mathematical Program with Linear Complementarity Constraints

SIAM Journal on Optimization
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study

Mathematical Programming: Series A and B
On Using the Elastic Mode in Nonlinear Programming Approaches to Mathematical Programs with Complementarity Constraints

SIAM Journal on Optimization
A two-sided relaxation scheme for Mathematical Programs with Equilibrium Constraints

SIAM Journal on Optimization
Interior Methods for Mathematical Programs with Complementarity Constraints

SIAM Journal on Optimization
A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

Journal of Global Optimization
The eigenvalue complementarity problem

Computational Optimization and Applications
A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations

Mathematical Programming: Series A and B
On the Global Solution of Linear Programs with Linear Complementarity Constraints

SIAM Journal on Optimization
Local minima of quadratic forms on convex cones

Journal of Global Optimization

The eigenvalue complementarity problem

Computational Optimization and Applications
Global optimization

Optimization Methods & Software - GLOBAL OPTIMIZATION
Cone-constrained eigenvalue problems: theory and algorithms

Computational Optimization and Applications
Reconstructing a matrix from a partial sampling of Pareto eigenvalues

Computational Optimization and Applications
A DC programming approach for solving the symmetric Eigenvalue Complementarity Problem

Computational Optimization and Applications
A new method for solving Pareto eigenvalue complementarity problems

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we discuss the eigenvalue complementarity problem (EiCP) where at least one of its defining matrices is asymmetric. A sufficient condition for the existence of a solution to the EiCP is established. The EiCP is shown to be equivalent to finding a global minimum of an appropriate merit function on a convex set Ω defined by linear constraints. A sufficient condition for a stationary point of this function on Ω to be a solution of the EiCP is presented. A branch-and-bound procedure is developed for finding a global minimum of this merit function on Ω. In addition, a sequential enumerative algorithm for the computation of the minimum and the maximum eigenvalues is also discussed. Computational experience is included to highlight the efficiency and efficacy of the proposed methodologies to solve the asymmetric EiCP.