Feasibility problems with complementarity constraints

R. Andreani, J.J. Júdice, J.M. Martínez and T. Martini

European Journal of Operational Research, 2016, vol. 249, issue 1, 41-54

Abstract: A Projected-Gradient Underdetermined Newton-like algorithm will be introduced for finding a solution of a Horizontal Nonlinear Complementarity Problem (HNCP) corresponding to a feasible solution of a Mathematical Programming Problem with Complementarity Constraints (MPCC). The algorithm employs a combination of Interior-Point Newton-like and Projected-Gradient directions with a line-search procedure that guarantees global convergence to a solution of HNCP or, at least, a stationary point of the natural merit function associated to this problem. Fast local convergence will be established under reasonable assumptions. The new algorithm can be applied to the computation of a feasible solution of MPCC with a target objective function value. Computational experience on test problems from well-known sources will illustrate the efficiency of the algorithm to find feasible solutions of MPCC in practice.

Keywords: Global optimization; Nonlinear programming; Nonlinear systems of equations; Complementarity problems; Mathematical Programming with Complementarity Constraints (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:249:y:2016:i:1:p:41-54

DOI: 10.1016/j.ejor.2015.09.030

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