An adaptive analog of Nesterov's method for variational inequalities with a strongly monotone operator
F.S. Stonyakin
V.I. Vernadsky Crimean Federal University, Simferopol, Russia, 295007
Keywords: вариационное неравенство, сильно монотонный оператор, адаптивный метод, условие Липшица, качество решения, variational inequality, strongly monotone operator, adaptive method, Lipschitz condition, solution quality
Abstract
An adaptive analog of the Nesterov method for variational inequalities with a strongly monotone operator is proposed. The main idea of the method proposed is the adaptive choice of constants in maximized concave functional at each iteration. In this case there is no need in specifying an exact value of this constant, because the method proposed makes possible to find a suitable constant at each iteration. Some estimates for the parameters determining the quality of the solution of the variational inequality depending on the number of iterations have been obtained.
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