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This article is cited in 5 scientific papers (total in 5 papers)
Penalty method with descent for problems of convex optiization
I. V. Konnov Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
Abstract:
We propose a penalty method for general convex constrained optimization problems, where each auxiliary penalized problem is replaced with an equivalent mixed variational inequality problem. This allows one to keep the decomposable structure of the initial problem and to simplify the direction finding subproblem. A gap function is utilized for evaluation of solution accuracy of the auxiliary penalized problem. Convergence of the method in primal and dual variables is established under rather weak assumptions.
Keywords:
convex optimization problem, non-linear constraints, penalty method, descent method, decomposition.
Received: 06.06.2018 Revised: 18.07.2018 Accepted: 26.09.2018
Citation:
I. V. Konnov, “Penalty method with descent for problems of convex optiization”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 7, 48–64; Russian Math. (Iz. VUZ), 63:7 (2019), 41–55
Linking options:
https://www.mathnet.ru/eng/ivm9482 https://www.mathnet.ru/eng/ivm/y2019/i7/p48
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