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A trust region method for solving generalized complementarity problems. (English) Zbl 0911.90324
Summary: 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.
Reviewer: Reviewer (Berlin)

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K10 Numerical optimization and variational techniques
Software:
PATH Solver
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