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

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

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Article ID: iaor20111373
Volume: 30
Issue: 2
Start Page Number: 285
End Page Number: 300
Publication Date: Nov 2004
Journal: Journal of Global Optimization
Authors:
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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