A Trust Region Method for Solving Generalized Complementarity Problems

Authors:
Houyuan Jiang;Masao Fukushima;Liqun Qi;Defeng Sun
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Optimization
Year:
1998

Citing 0
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Abstract

Based on a semismooth equation reformulation using Fischer's function, a trust region algorithm is proposed for solving the generalized complementarity problem (GCP). The algorithm uses a generalized Jacobian of the function involved in the semismooth equation and adopts the squared natural residual of the semismooth equation as a merit function. The proposed algorithm is applicable to the nonlinear complementarity problem because the latter problem is a special case of the GCP. Global convergence and, under a nonsingularity assumption, local Q-superlinear (or quadratic) convergence of the algorithm are established. Moreover, calculation of a generalized Jacobian is discussed and numerical results are presented.