This article is cited 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.

UDC: 519.85

Received: 06.06.2018
Revised: 18.07.2018
Accepted: 26.09.2018

DOI: 10.26907/0021-3446-2019-7-48-64

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:7, 41–55

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