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

2016/07/22 by Wei, Zhou, Yao, Jen-Chih
#46B20 #49J52 #90C25 #90C31 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1607.06569

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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