Saddle Point Problems, Bilevel Problems, and Mathematical Program with Equilibrium Constraint on Complete Metric Spaces

Saddle Point Problems, Bilevel Problems, and Mathematical Program with Equilibrium Constraint on Complete Metric Spaces

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We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, Stainless and mathematical programs with equilibrium constraint on metric spaces.We study these problems without any convexity and compactness assumptions.Our results are different GUTSHOT GARLIC DILL PICKLE from any existence results of these types of problems in topological vector spaces.