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MODIFIED DESCENT METHODS FOR SOLVING MONOTONE VARIATIONAL INEQUALITIES

Dexiang Zhu, Patrice Marcotte

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Abstract

Recently, Fukushima proposed a differentaible optimization framework for solving strictly monotone and continuously differentiable variational inequalities. the main result of this paper is to show that the strict monotonicity assumption can be removed, if one is willing to modify slightly the basic algorithmic scheme. The modification applies also to a general descent scheme introduced by Zhu and Marcotte. (A)

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What this paper is about

Recently, Fukushima proposed a differentaible optimization framework for solving strictly monotone and continuously differentiable variational inequalities. the main result of this paper is to show that the strict monotonicity assumption can be removed, if one is willing to modify slightly the basic algorithmic scheme. The modification applies also to a general descent scheme introduced by Zhu and Marcotte. (A)

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Available abstract

Recently, Fukushima proposed a differentaible optimization framework for solving strictly monotone and continuously differentiable variational inequalities. the main result of this paper is to show that the strict monotonicity assumption can be removed, if one is willing to modify slightly the basic algorithmic scheme. The modification applies also to a general descent scheme introduced by Zhu and Marcotte. (A)

Key concepts: Variational inequality, Monotone polygon, Monotonic function, Differentiable function, Mathematics, Descent (aeronautics), Scheme (mathematics), Mathematical optimization

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