In this paper a characterization of the local-nonglobal minimizes 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 minimizes and that the Lagrange multiplier that corresponds to this minimizes is the largest solution of a nonlinear scalar equation. An algorithm is proposed for computing the local-nonglobal minimizes.
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J. M. Martı́nez (1994) studied this question.
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