TY - JOUR

T1 - Exact penalty functions in isoperimetric problems

AU - Demyanov, V. F.

AU - Tamasyan, G.Sh.

PY - 2011

Y1 - 2011

N2 - It was earlier demonstrated, by the so-called main (or simplest) problem of the Calculus of Variations, that the Theory of Exact Penalties allows one not only to derive fundamental results of the Calculus of Variations but also to construct new direct numerical methods for solving variational problems based on the notions of subgradient and hypogradient of the exact penalty function (which is essentially nonsmooth even if all initial data are smooth). In this article Exact Penalties are used to solve isoperimetric problems of the Calculus of Variations. New direct numerical methods are described (e.g. the method of hypodifferential descent). Several numerical examples are discussed.

AB - It was earlier demonstrated, by the so-called main (or simplest) problem of the Calculus of Variations, that the Theory of Exact Penalties allows one not only to derive fundamental results of the Calculus of Variations but also to construct new direct numerical methods for solving variational problems based on the notions of subgradient and hypogradient of the exact penalty function (which is essentially nonsmooth even if all initial data are smooth). In this article Exact Penalties are used to solve isoperimetric problems of the Calculus of Variations. New direct numerical methods are described (e.g. the method of hypodifferential descent). Several numerical examples are discussed.

KW - calculus of variations

KW - isoperimetric problems

KW - Exact Penalties

KW - Nonsmooth Analysis

KW - subdifferential

KW - method of hypodifferential descent

U2 - 10.1080/02331934.2010.534166

DO - 10.1080/02331934.2010.534166

M3 - Article

VL - 60

SP - 153

EP - 177

JO - Optimization

JF - Optimization

SN - 0233-1934

IS - 1

ER -