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A canonical duality approach for the solution of affine quasi-variational inequalities. (English) Zbl 1354.90148
The authors consider quasi-variational inequality problems where both the cost and constraint mappings are affine. This property allows them to write the optimality conditions involving the usual complementarity problem. Using the Fischer-Burmeister gap function, they rewrite the optimality conditions as an unconstrained optimization problem and propose its several reformulations by using the so-called canonical duality approach. The authors give some relationships among stationary points of these problems and conditions for recognizing the global solutions. A heuristic algorithm based on these properties is suggested. Its performance is illustrated by computational experiments.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C46 Optimality conditions and duality in mathematical programming
90C26 Nonconvex programming, global optimization
Software:
PATH Solver; QVILIB
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References:
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