Programming approach to Malfatti’s problem
Автор: Enkhbat Rentsen, Barkova Mariya V., Sukhee Batbileg
Журнал: Вестник Бурятского государственного университета. Математика, информатика @vestnik-bsu-maths
Рубрика: Управляемые системы и методы оптимизации
Статья в выпуске: 4, 2018 года.
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In previous works R. Enkhbat showed that the Malfatti's problem can be treated as the convex maximization problem and provided with an algorithm based on Global Optimality Conditions of A. S. Strekalovsky. In this article we reformulate Malfatti’s problem as a D.C. programming problem with a nonconvex constraint. The reduced problem as an optimization problem with D.C. constraints belongs to a class of global optimization. We apply the local and global optimality conditions by A. 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 problem. In numerical experiments, initial points of the proposed algorithm are chosen randomly. Global solutions have been found in all cases.
D.c. programming, global optimality conditions, malfatti''s problem, convex maximization, local search algorithm, d.c. constraint, global optimization, malfatti circles, linearized problem, d.c. minimization, d.c. оптимизация, d.c. ограничение, d.c. минимизация
Короткий адрес: https://sciup.org/148308922
IDR: 148308922 | DOI: 10.18101/2304-5728-2018-4-72-83
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