Abstract
We propose a penalty method for general convex constrained optimization problems, where each auxiliary penalized problem is solved approximately with a special composite descent method. Direction finding choice in this method is found with the help of an equivalent equilibrium type problem. This allows one to keep the complete structure of the initial problem, although without nonlinear constraints and to simply calculate the descent direction in separable problems. Convergence of the method in primal and dual variables is established under rather weak assumptions.
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 7, pp. 48–64.
Funding
The results of this work were obtained within the state assignment of the Ministry of Science and Education of Russia, project no. 1.460.2016/1.4. In this work, the author was also funded by Russian Foundation for Basic Research, project no. 16-01-00408a and by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project no. 1.12878.2018/12.1.
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Konnov, I.V. An Approximate Penalty Method with Descent for Convex Optimization Problems. Russ Math. 63, 41–55 (2019). https://doi.org/10.3103/S1066369X19070053
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DOI: https://doi.org/10.3103/S1066369X19070053