Approximate inertial proximal methods using the enlargement of maximal monotone operators

Abstract : An approximate procedure for solving the problem of nding a zero of a maximal monotone operator is proposed and its convergence is established under various conditions. More precisely, it is shown that this method weakly converges under natural assumptions and strongly converges provided that either the inverse of the involved operator is Lipschitz continuous around zero or the interior of the solution set is nonempty. A particular attention is given to the convex minimization case. AMS Subject Classication : Primary, 90C ; Secondary, 49M45, 65C.
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International Journal of Pure and Applied Mathematics, Academic Publishing Ltd, 2003, 5 (3), pp.283-299
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Abdellatif Moudafi, E. Elizabeth. Approximate inertial proximal methods using the enlargement of maximal monotone operators. International Journal of Pure and Applied Mathematics, Academic Publishing Ltd, 2003, 5 (3), pp.283-299. 〈hal-00779255〉

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