Abstract
We present a framework for descent algorithms that solve the monotone variational inequality problem VIP v which consists in finding a solutionv *∈Ω v satisfyings(v *)T(v−v *)⩾0, for allv∈Ω 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.
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This research was supported in part by individual operating grants from NSERC.
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Wu, J.H., Florian, M. & Marcotte, P. A general descent framework for the monotone variational inequality problem. Mathematical Programming 61, 281–300 (1993). https://doi.org/10.1007/BF01582152
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DOI: https://doi.org/10.1007/BF01582152