Feasibility problems with complementarity constraints

•Computing a Simple Feasible Solution of MPCC.•Computing a Target Feasible Solution of MPCC.•Convergence of a PGIP Algorithm for an Underdetermined Complementarity Problem. A Projected-Gradient Underdetermined Newton-like algorithm will be introduced for finding a solution of a Horizontal Nonlinear...

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Vydané v:European journal of operational research Ročník 249; číslo 1; s. 41 - 54
Hlavní autori: Andreani, R., Júdice, J.J., Martínez, J.M., Martini, T.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 16.02.2016
Elsevier Sequoia S.A
Predmet:
Algorithms
Combinatorics
Complementarity problems
Global optimization
Mathematical functions
Mathematical problems
Mathematical programming
Mathematical Programming with Complementarity Constraints
Nonlinear programming
Nonlinear systems of equations
Studies
Nonlinear systems of equations
Global optimization
Nonlinear programming
Complementarity problems
Mathematical Programming with Complementarity Constraints
ISSN:0377-2217, 1872-6860
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Popis
Shrnutí:•Computing a Simple Feasible Solution of MPCC.•Computing a Target Feasible Solution of MPCC.•Convergence of a PGIP Algorithm for an Underdetermined Complementarity Problem. 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.
Bibliografia:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2015.09.030