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

Authors:
Paul Tseng
Affiliations:
Department of Mathematics, University of Washington, Seattle, U.S.A. ( 98195
Venue:
Journal of Global Optimization
Year:
2004

Citing 18
Cited 3

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Global Convergence of the Affine Scaling Algorithm for Convex Quadratic Programming

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Abstract

We study convergence properties of Dikin驴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.