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Global and Local Search Methods for D.C. Constrained Problems

Авторы: Strekalovsky A.S.

Журнал: Lecture Notes in Computer Science

Том: 12095

Номер:

Год: 2020

Отчётный год: 2020

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Местоположение издательства:

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Проекты:

DOI: 10.1007/978-3-030-49988-4_1

Аннотация: This paper addresses the general optimization problem ($$\mathcal P$$) with equality and inequality constraints and the cost function given by d.c. functions. We reduce the problem to a penalized problem ($$\mathcal P_{\sigma }$$) without constraints with the help of the Exact Penalization Theory. Further, we show that the reduced problem is also a d.c. minimization problem. This property allows us to prove the Global Optimality Conditions (GOCs), which reduce the study of the penalized problem to an investigation of a family of linearized (convex) problems tractable with the help of standard convex optimization methods and software. In addition, we propose a new Local Search Scheme (LSS1) which produces a sequence of vectors converging to a so-called critical point. On the other hand, the vector satisfying the GOCs turns out to be also a critical point. On the basis of the GOCs for finding a global solution to ($$\mathcal P_{\sigma }$$), we develop a Global Search Scheme, including the LSS1 with an update of the penalty parameter, and a special stopping criteria allowing detection of a feasible vector in the original problem ($$\mathcal P$$), and, consequently, a global solution to the original Problem ($$\mathcal P$$).

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет

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