Monday , April 22 2024

Optimization of a Constrained Quadratic Function

Department of Mathematics and Computer Science
PO Box 3517 Saint Mary’s College of California,
Moraga, CA,94575

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.

>>Full text
Charles HAMAKER, Optimization of a Constrained Quadratic Function, Studies in Informatics and Control, ISSN 1220-1766, vol. 18 (1), pp. 21-32, 2009.