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Metrically convex functions in normed spaces

Stanisław Kryński — 1993

Studia Mathematica

Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.

Minimization of a concave function on a convex polyhedron

Stanisław L. Kryński — 1982

Mathematica Applicanda

The problem of minimizing a concave function on a convex polyhedron is considered. The author proposes a solution algorithm which, starting from a vertex representing a local minimum of the objective function, constructs a sequence of auxiliary linear programming problems in order to find a global minimum. The convergence of the algorithm is proven.

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