A general descent framework for the monotone variational inequality problem |
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Authors: | Jia Hao Wu Michael Florian Patrice Marcotte |
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Institution: | (1) Centre de recherche sur les transports, Université de Montréal, C.P. 6128, H3C 3J7 Succursale, Montréal, Qué., Canada |
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Abstract: | We present a framework for descent algorithms that solve the monotone variational inequality problem VIP
v
which consists in finding a solutionv
*![isin](/content/g4m37n6110661u31/xxlarge8712.gif)
v satisfyings(v
*)T(v–v
*) 0, for allv![isin](/content/g4m37n6110661u31/xxlarge8712.gif)
v. This unified framework includes, as special cases, some well known iterative methods and equivalent optimization formulations. A descent method is developed for an equivalent general optimization formulation and a proof of its convergence is given. Based on this unified logarithmic framework, we show that a variant of the descent method where each subproblem is only solved approximately is globally convergent under certain conditions.This research was supported in part by individual operating grants from NSERC. |
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Keywords: | Variational inequalities descent methods optimization |
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