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AN EXTENDED DESCENT FRAMEWORK FOR MONOTONE VARIATIONAL INEQUALITIES

Dexiang Zhu, Patrice Marcotte

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Abstract

In this paper, the authors develop a very general descent framework for solving asymetric, monotone variational inequalities. They introduce two classes of differentiable merit functions and the associated global convergence frameworks which include, as special instances, the projection, Newton, quasi-Newton, linear Jacobi and nonlinear methods. The generic algorithm is very flexible and consequently well suited for exploiting any particular structure of the problem. (A)

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What this paper is about

In this paper, the authors develop a very general descent framework for solving asymetric, monotone variational inequalities. They introduce two classes of differentiable merit functions and the associated global convergence frameworks which include, as special instances, the projection, Newton, quasi-Newton, linear Jacobi and nonlinear methods. The generic algorithm is very flexible and consequently well suited for exploiting any particular structure of the problem. (A)

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, the authors develop a very general descent framework for solving asymetric, monotone variational inequalities. They introduce two classes of differentiable merit functions and the associated global convergence frameworks which include, as special instances, the projection, Newton, quasi-Newton, linear Jacobi and nonlinear methods. The generic algorithm is very flexible and consequently well suited for exploiting any particular structure of the problem. (A)

Key concepts: Variational inequality, Monotone polygon, Differentiable function, Mathematics, Convergence (economics), Descent (aeronautics), Mathematical optimization, Descent direction

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