Abstract
The aim of the paper is to show how to explicitly express the function of sectional curvature with the first and second derivatives of the problem’s functions in the case of submanifolds determined by equality constraints in the n-dimensional Euclidean space endowed with the induced Riemannian metric, which is followed by the formulation of the minimization problem of sectional curvature at an arbitrary point of the given submanifold as a global minimization one on a Stiefel manifold. Based on the results, the sectional curvatures of Stiefel manifolds are analysed and the maximal and minimal sectional curvatures on an ellipsoid are determined.
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This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA-T043276 and OTKA-K60480.
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Rapcsák, T. Sectional curvatures in nonlinear optimization. J Glob Optim 40, 375–388 (2008). https://doi.org/10.1007/s10898-007-9212-7
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DOI: https://doi.org/10.1007/s10898-007-9212-7