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Solving mathematical programs with equilibrium constraints as constrained equations, preprint 2010
"... The paper studies three classes of optimization problems with bilevel structure including mathematical programs with equilibrium constraints (MPEC) and semiinfinite problems (SIP). The main goal of the paper is to provide results which establish the existence of feasible points of the problems. Th ..."
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The paper studies three classes of optimization problems with bilevel structure including mathematical programs with equilibrium constraints (MPEC) and semiinfinite problems (SIP). The main goal of the paper is to provide results which establish the existence of feasible points of the problems. These results are based on the socalled KKM Lemma. We are also interested in the convexity properties of these problems.
The Equilibrium Equivalent Representation for Variational Inequalities Problems with Its Application in Mixed Traffic Flows
"... Abstract In this paper, we first introduce the relationship between the HartmanStampacchia variational inequalities (VI) problems and equilibrium programming (EP), and we present EP equivalent representation for HartmanStampacchia VI problems. After analyze and discuss the condition for optimizati ..."
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Abstract In this paper, we first introduce the relationship between the HartmanStampacchia variational inequalities (VI) problems and equilibrium programming (EP), and we present EP equivalent representation for HartmanStampacchia VI problems. After analyze and discuss the condition for optimization of EP, and the relation with the model transformation equivalent applied in mixed traffic assignment problems (MTAP). Finally we give an optimal model and effective algorithm for MTAP.