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Global linear convergence of a path-following algorithm for some monotone variational inequality problems

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Abstract

We consider a primal-scaling path-following algorithm for solving a certain class of monotone variational inequality problems. Included in this class are the convex separable programs considered by Monteiro and Adler and the monotone linear complementarity problem. This algorithm can start from any interior solution and attain a global linear rate of convergence with a convergence ratio of 1 −c/√m, wherem denotes the dimension of the problem andc is a certain constant. One can also introduce a line search strategy to accelerate the convergence of this algorithm.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, Washington

    P. Tseng (Assistant Professor)

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  1. P. Tseng
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Communicated by O. L. Mangasarian

The author gratefully thanks one of the referees for bringing to his attention related works and for suggesting ways to prove (10) without making the assumption, made in the original manuscript, that ∇f be symmetric wheneverA is not the null matrix.

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Tseng, P. Global linear convergence of a path-following algorithm for some monotone variational inequality problems. J Optim Theory Appl 75, 265–279 (1992). https://doi.org/10.1007/BF00941467

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