Hybrid approach with active set identification for mathematical programs with complementarity constraints

We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2006, Vol.128 (1), p.1-28
Main Authors: LIN, G. H, FUKUSHIMA, M
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Applied sciences
Continuation methods
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematical programming
Methods
Nonlinearity
Operational research and scientific management
Operational research. Management science
Optimization
Smoothing
Strategy
Studies
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Summary:We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination property. Further discussions and numerical experience are given as well. [PUBLICATION ABSTRACT]
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-005-7549-y