Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization
Abstract
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces. The established conditions are expressed in terms of second-order subdifferentials of lower semicontinuous functions and mainly concern prox-regular objectives that cover a large territory in nonsmooth optimization and its applications. Our tools are based on the machinery of variational analysis and second-order generalized differentiation. The obtained general results are applied to problems of nonlinear programming, where the derived second-order optimality conditions are new even for problems with twice continuously differential data, being expressed there in terms of the classical Hessian matrices.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2023
- DOI:
- 10.48550/arXiv.2312.16277
- arXiv:
- arXiv:2312.16277
- Bibcode:
- 2023arXiv231216277D
- Keywords:
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- Mathematics - Optimization and Control