Abstract:
The paper addresses a nonconvex nonsmooth optimization problem with the cost function and equality and inequality constraints given by d.c. functions, i.e., functions representable as the difference of convex functions. The original problem is reduced to a problem without constraints with the help of exact penalization theory. Then the penalized problem is represented as a d.c. minimization problem without constraints, for which new mathematical tools are developed in the form of global optimality conditions (GOCs). The GOCs reduce the nonconvex problem in question to a family of linearized (convex) problems and are used to derive a nonsmooth form of the Karush-Kuhn-Tucker theorem for the original problem. In addition, the GOCs possess a constructive (algorithmic) property, which makes it possible to leave the local pits and stationary (critical) points of the original problem. The effectiveness of the GOCs is demonstrated with examples.
Citation:
A. S. Strekalovskii, “New global optimality conditions in a problem with d.c. constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 1, 2019, 245–261
\Bibitem{Str19}
\by A.~S.~Strekalovskii
\paper New global optimality conditions in a problem with d.c. constraints
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 1
\pages 245--261
\mathnet{http://mi.mathnet.ru/timm1614}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-1-245-261}
\elib{https://elibrary.ru/item.asp?id=37051109}
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https://www.mathnet.ru/eng/timm1614
https://www.mathnet.ru/eng/timm/v25/i1/p245
This publication is cited in the following 6 articles:
A. S. Strekalovskii, M. V. Barkova, “O reshenii sistem kvadratichnykh uravnenii”, Tr. IMM UrO RAN, 30, no. 2, 2024, 173–187
Mengkezhula Sagaarenchen, Batbileg Sukhee, Enkhbat Rentsen, Battur Gompil, “D. C. optimization approach for finding Berge equilibrium in bimatrix game”, NACO, 2024
A. S. Strekalovskii, “Minimizing Sequences in a Constrained DC Optimization Problem”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S255–S278
A. S. Strekalovskii, “Elementy globalnogo poiska v obschei zadache d.c. optimizatsii”, Differentsialnye uravneniya i optimalnoe upravlenie, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 196, VINITI RAN, M., 2021, 114–127
A. S. Strekalovsky, Lecture Notes in Computer Science, 12755, Mathematical Optimization Theory and Operations Research, 2021, 17
A. S. Strekalovsky, “On a global search in dc optimization problems”, Optimization and Applications, Optima 2019, Communications in Computer and Information Science, 1145, eds. M. Jacimovic, M. Khachay, V. Malkova, M. Posypkin, Springer, 2020, 222–236
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