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Bibliographic description:
Enkhbat R.
,
Barkova M. V.
,
Batblleg S.
D.C. PROGRAMMING APPROACH ТО МALFATTI'S PROBLEM // BSU bulletin. Mathematics, Informatics. - 2018. №4. . - С. 72-83.
Title:
D.C. PROGRAMMING APPROACH ТО МALFATTI'S PROBLEM
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-4-72-83UDK: 519.853
Annotation:
In previous works R. Enkhbat showed that the Malfatti's proЫem can Ье treated as the convex maximization proЫem and provided with an algorithm based on Global Optimality Conditions of А S. Strekalovsky. In this article we reformulate Mal­ fatti's proЫem as а D.C. programming proЫem with а nonconvex constraint. Тhе reduced proЫem as an optimization proЫem with D.C. constraints belongs to а class of global optimization. We apply the local and global optimality conditions Ьу А S. Strekalovsky developed for D.C programming. Based on local search methods for D.C. programming, we have developed an algorithm for numerical solution of Malfatti's proЫem. 1n numerical experiments, initial points of the proposed algo­ rithm are chosen randomly. Global solutions have been found in all cases.
Keywords:
D.C. programming; global optimality conditions; Malfatti's proЫem; convex maximization; local search algorithm; D.C. constraint, global optimization, Malfatti circles; linearized proЫem; D.C. minimization.
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