Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910772729217024 |
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| author | Khanh, Pham Duy Khoa, Vu Vinh Huy Mordukhovich, Boris S. Phat, Vo Thanh |
| author_facet | Khanh, Pham Duy Khoa, Vu Vinh Huy Mordukhovich, Boris S. Phat, Vo Thanh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16277 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization Khanh, Pham Duy Khoa, Vu Vinh Huy Mordukhovich, Boris S. Phat, Vo Thanh Optimization and Control 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. |
| title | Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2312.16277 |