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Linearly convergent descent methods for the unconstrained minimization of convex quadratic splines

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Abstract

We propose two linearly convergent descent methods for finding a minimizer of a convex quadratic spline and establish global error estimates for the iterates. One application of such descent methods is to solve convex quadratic programs, since they can be reformulated as problems of unconstrained minimization of convex quadratic splines. In particular, we derive several new linearly convergent algorthms for solving convex quadratic programs. These algorithms could be classified as row-action methods, matrix-splitting methods, and Newton-type methods.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia

    W. Li (Assistant Professor)

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  1. W. Li
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Communicated by P. Tseng

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Li, W. Linearly convergent descent methods for the unconstrained minimization of convex quadratic splines. J Optim Theory Appl 86, 145–172 (1995). https://doi.org/10.1007/BF02193464

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