Local Minimizers of Quadratic Functions on Euclidean Balls and Spheres

1 February 1994

journal article
research article
Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization

Vol. 4 (1) , 159-176
https://doi.org/10.1137/0804009

Abstract

In this paper a characterization of the local-nonglobal minimizer of a quadratic function defined on a Euclidean ball or a sphere is given. It is proven that there exists at most one local-nonglobal minimizer and that the Lagrange multiplier that corresponds to this minimizer is the largest solution of a nonlinear scalar equation. An algorithm is proposed for computing the local-nonglobal minimizer.

Keywords

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