TY - JOUR

T1 - On the Quadratic Eigenvalue Complementarity Problem over a general convex cone

AU - Brás, Carmo P.

AU - Fukushima, Masao

AU - Iusem, Alfredo N.

AU - Júdice, Joaquim J.

N1 - Sem PDF

PY - 2015/11/15

Y1 - 2015/11/15

N2 - The solution of the Conic Quadratic Eigenvalue Complementarity Problem (CQEiCP) is first investigated without assuming symmetry on the matrices defining the problem. A new sufficient condition for existence of solutions of CQEiCP is presented, extending to arbitrary pointed, closed and convex cones a condition known to hold when the cone is the nonnegative orthant. We also address the symmetric CQEiCP where all its defining matrices are symmetric. We show that, assuming that two of its defining matrices are positive definite, this symmetric CQEiCP reduces to the computation of a stationary point of an appropriate merit function on a convex set. Furthermore, we discuss the use of the so called Spectral Projected Gradient (SPG) algorithm for solving CQEiCP when the cone of interest is the second-order cone (SOCQEiCP). A new algorithm is designed for the computation of the projections required by the SPG method to deal with SOCQEiCP. Numerical results are included to illustrate the efficiency of the SPG method and the new projection technique in practice.

AB - The solution of the Conic Quadratic Eigenvalue Complementarity Problem (CQEiCP) is first investigated without assuming symmetry on the matrices defining the problem. A new sufficient condition for existence of solutions of CQEiCP is presented, extending to arbitrary pointed, closed and convex cones a condition known to hold when the cone is the nonnegative orthant. We also address the symmetric CQEiCP where all its defining matrices are symmetric. We show that, assuming that two of its defining matrices are positive definite, this symmetric CQEiCP reduces to the computation of a stationary point of an appropriate merit function on a convex set. Furthermore, we discuss the use of the so called Spectral Projected Gradient (SPG) algorithm for solving CQEiCP when the cone of interest is the second-order cone (SOCQEiCP). A new algorithm is designed for the computation of the projections required by the SPG method to deal with SOCQEiCP. Numerical results are included to illustrate the efficiency of the SPG method and the new projection technique in practice.

KW - Complementarity problems

KW - Eigenvalue problems

KW - Global optimization

KW - Nonlinear programming

UR - http://www.scopus.com/inward/record.url?scp=84943279676&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2015.09.014

DO - 10.1016/j.amc.2015.09.014

M3 - Article

AN - SCOPUS:84943279676

VL - 271

SP - 594

EP - 608

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -