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Approximation of convex functions by projections of polyhedra

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Abstract

A method for approximate solution of minimization problems for multivariable convex functions with convex constraints is proposed. The main idea consists in approximation of the objective function and constraints by piecewise linear functions and subsequent reduction of the initial convex programming problem to a problem of linear programming. We present algorithms constructing approximating polygons for some classes of single variable convex functions. The many-dimensional problem is reduced to a one-dimensional one by an inductive procedure. The efficiency of the method is illustrated by numerical examples.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    E. S. Gorskaya

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  1. E. S. Gorskaya
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Original Russian Text © E.S.Gorskaya, 2010, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2010, Vol. 65, No. 5, pp. 20–27.

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Gorskaya, E.S. Approximation of convex functions by projections of polyhedra. Moscow Univ. Math. Bull. 65, 196–203 (2010). https://doi.org/10.3103/S0027132210050049

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