Duality and Lipschitzian selections in best approximation from nonconvex cones

Abstract Duality relationships in finding a best approximation from a nonconvex cone in a normed linear space in general and in the space of bounded functions in particular, are investigated. The cone and the dual problems are defined in terms of positively homogeneous super-additive functional on the space. Conditions are developed on the cone so that the duality gap between a pair of primal and dual problems does not exist. In addition, Lipschitz continuous selections of the metric projection are identified. The results are specialized to a convex cone. Applications are indicated to approximation problems.

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