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arXiv · 1607.06569

Second-order Optimality Conditions by Generalized Derivatives and Applications in Hilbert Spaces

Zhou Wei·Jen-Chih Yao
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Abstract

In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality conditions for paraconcave functions. As applications, we use these second-order optimality conditions to study strict local minimizers of order two and provide sufficient and/or necessary conditions for ensuring the local minimizer. This work extends and generalizes the study on second-order optimality conditions from the finite-dimensional space to the Hilbert space.

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Zhou Wei, Jen-Chih Yao. 2016-07-22. Second-order Optimality Conditions by Generalized Derivatives and Applications in Hilbert Spaces. https://arxiv.org/abs/1607.06569

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