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Titlebook: Optimization with Multivalued Mappings; Theory, Applications Stephan Dempe,Vyacheslav Kalashnikov Book 2006 Springer-Verlag US 2006 Bilevel

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Complementarity constraints as nonlinear equations: Theory and numerical experienceograms. This paper examines various nonlinear formulations of the complementarity constraints. Several nonlinear complementarity functions are considered for use in MPCC. Unlike standard smoothing techniques, however, the reformulations do not require the control of a smoothing parameter. Thus they
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Optimality conditions for a d.c. set-valued problem via the extremal principleconomics, engineering and human decision-making. Using an . introduced by Mordukhovich, we establish optimality conditions for D.C. ( difference of convex ) set-valued optimization problems. An application to vector fractional mathematical programming is also given.
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Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities by computing the fixed point of a certain multivalued mapping having a contraction selection. Moreover a solution of a multivalued cocoercive variational inequality can be computed by finding a fixed point of a certain mapping having nonexpansive selection. By the Banach contraction mapping principle it is easy to establish the convergence rate.
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Optimality conditions for a d.c. set-valued problem via the extremal principleconomics, engineering and human decision-making. Using an . introduced by Mordukhovich, we establish optimality conditions for D.C. ( difference of convex ) set-valued optimization problems. An application to vector fractional mathematical programming is also given.
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Path-based formulations of a bilevel toll setting problemA version of the toll setting problem consists in determining profit maximizing tolls on a subset of arcs of a transportation network, given that users travel on shortest paths. This yields a bilevel program for which we propose efficient algorithms based on path generation.
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