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A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions. (English) Zbl 1393.90122
Summary: We study an unconstrained minimization approach to the generalized complementarity problem \(\mathrm{GCP}(f,g)\) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are \(C^1\). Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to \(f\) and \(g\) leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for \(\mathrm{GCP}(f,g)\) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.
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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