Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives
Author
dc.contributor.author
Khanh, Pham Duy
Author
dc.contributor.author
Phat, Vo Thanh
Admission date
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2020-05-08T13:32:06Z
Available date
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2020-05-08T13:32:06Z
Publication date
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2020
Cita de ítem
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Optimization Letters Mar 2020
es_ES
Identifier
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10.1007/s11590-020-01563-6
Identifier
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https://repositorio.uchile.cl/handle/2250/174566
Abstract
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For a C-2-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for C-1,C-1-smooth functions by using the Frechet and Mordukhovich second-order subdifferentials.