Application of One Class of Penalty Functions for Solving Variation Problems
Abstract
Application of penalty function methods for nonlinear constrained extremum problems allows using unconstrained optimization methods. In this direction, the works of such authors as A.V. Fiacco, G.P. McCormick, J. Cea, E. Polak, I.I. Eremin, B.T. Polyak and others are well known. Investigation of the penalty function method convergence for convex programming problems with a finite number of constraints is the most complete in the literature. In this case, a completely defined range of functions is considered as a penalty.
We consider the minimization problem of non-linear convex functional on the convex closed set of Sobolev spaces. To solve this problem, one class of integral penalty functions introduced in papers by A.A. Kaplan is used. This leads to extremum problem on the whole Sobolev space. The estimation of convergence rate of the penalty method with integral penalty functions is obtained by generalizing the investigation methods for the case of a finite number of restrictions on the case of integral penalty functions. The obtained results can be used in numerical studies of similar problems.
DOI 10.14258/izvasu(2018)1-22
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Copyright (c) 2018 Т.В. Саженкова, А.Н. Саженков, Е.А. Плотникова
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