A Version of the Mirror descent Method to Solve Variational Inequalities*
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Nemirovski and Yudin proposed the mirror descent algorithm at the late 1970s to solve convex optimization problems. This method is suitable to solve huge-scale optimization problems. In the paper, we describe a new version of the mirror descent method to solve variational inequalities with pseudomonotone operators. The method can be interpreted as a modification of Popov’s two-step algorithm with the use of Bregman projections on the feasible set. We prove the convergence of the sequences generated by the proposed method.
Keywordsvariational inequality pseudomonotonicity Bregman distance Kullback–Leibler distance mirror descent method convergence
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