Unconstrained methods for nonsmooth nonlinear complementary problems

We consider a nonsmooth nonlinear complementarity problem when the underlying functions admit the H-differentiability but not necessarily locally Lipschitzian nor directionally differentiable. We study the connection between the solutions of the nonsmooth nonlinear complementarity problem and global/local/stationary points ofthe associated square penalized Fischer-Burmeister and square Kanzow-Kleinmichel merit functions. We show under appropriate regularity conditions on an H-differential of f, minimizing a merit function corresponding to f,leads to a solution of the nonlinearcomplementarity problem.

Article originally published in ‘AMO Advanced Modeling and Optimization’, V. 12(2010), n. 1, pp. 20-35. Reprinted with permission.

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