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A new derivative-free descent method for the nonlinear complementarity problem. (English) Zbl 0996.90085

Di Pillo, Gianni (ed.) et al., Nonlinear optimization and related topics. Workshop, Erice, Sicily, Italy, June 23-July 2, 1998. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 36, 463-487 (2000).
Summary: Recently, much effort has been made in solving and analyzing the Nonlinear Complementarity Problem (NCP) by means of a reformulation of the problem as an equivalent unconstrained optimization problem involving a merit function. In this paper, we propose a new merit function for the NCP and show several favorable properties of the proposed function. In particular, we give conditions under which the function provides a global error bound for the NCP and conditions under which its level sets are bounded. Moreover, we propose a new derivative-free descent algorithm for solving the NCP based on this function. We show that any accumulation point generated by the algorithm is a solution of the NCP under the monotonicity assumption on the problem. Also, we prove that the sequence generated by the algorithm converges linearly to the solution under the strong monotonicity assumption.
For the entire collection see [Zbl 0949.00039].

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C56 Derivative-free methods and methods using generalized derivatives
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