Friday , September 21 2018

Optimization of a Constrained Quadratic Function

Charles HAMAKER
Department of Mathematics and Computer Science
PO Box 3517 Saint Mary’s College of California,
Moraga, CA,94575
chamaker@stmarys-ca.edu

Dedicated on the occasion of his 60th birthday to Neculai Andrei in appreciation of a lifetime of contributions to mathematics, as a productive researcher, an author of valuable texts and software, and a leader in the mathematical community.

Abstract: For A a positive definite, symmetric n x n matrix and b a real n-vector, the objective function Image826-2009,1,2 is optimized over the unit sphere. The proposed iterative methods, based on the gradient of f, converge in general for maximization and for large |b| for minimization with the principal computational cost being one or two matrix-vector multiplications per iteration. The rate of convergence improves as |b| increases, becoming computationally competitive in that case with algorithms developed for the more general problem wherein A may be indefinite.

Keywords: Constrained optimization, quadratic functions, iterated gradients, acceleration of convergence.

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CITE THIS PAPER AS:
Charles HAMAKER, Optimization of a Constrained Quadratic Function, Studies in Informatics and Control, ISSN 1220-1766, vol. 18 (1), pp. 21-32, 2009.