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Convergence Properties of Dikin’s Affine Scaling Algorithm for Nonconvex Quadratic Minimization

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Abstract

We study convergence properties of Dikin’s affine scaling algorithm applied to nonconvex quadratic minimization. First, we show that the objective function value either diverges or converges Q-linearly to a limit. Using this result, we show that, in the case of box constraints, the iterates converge to a unique point satisfying first-order and weak second-order optimality conditions, assuming the objective function Hessian Q is rank dominant with respect to the principal submatrices that are maximally positive semidefinite. Such Q include matrices that are positive semidefinite or negative semidefinite or nondegenerate or have negative diagonals. Preliminary numerical experience is reported.

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  1. Department of Mathematics, University of Washington, Seattle, Washington, 98195, U.S.A. (

    Paul Tseng

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  1. Paul Tseng
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Tseng, P. Convergence Properties of Dikin’s Affine Scaling Algorithm for Nonconvex Quadratic Minimization. J Glob Optim 30, 285–300 (2004). https://doi.org/10.1007/s10898-004-8276-x

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