A strong second-order sequential optimality condition for nonlinear programming problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909521508564992 |
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| author | Li, Huimin Yamakawa, Yuya Fukuda, Ellen H. Yamashita, Nobuo |
| author_facet | Li, Huimin Yamakawa, Yuya Fukuda, Ellen H. Yamashita, Nobuo |
| contents | Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint qualifications (CQ) are not met. Recent advances in sequential optimality conditions address this limitation in both first- and second-order cases, providing genuine optimality guarantees at local optima, even when CQs do not hold. However, some second-order sequential optimality conditions still require some restrictive conditions on constraints in the recent literature. In this paper, we propose a new strong second-order sequential optimality condition without CQs. We also show that a penalty-type method and an augmented Lagrangian method generate points satisfying these new optimality conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A strong second-order sequential optimality condition for nonlinear programming problems Li, Huimin Yamakawa, Yuya Fukuda, Ellen H. Yamashita, Nobuo Optimization and Control Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint qualifications (CQ) are not met. Recent advances in sequential optimality conditions address this limitation in both first- and second-order cases, providing genuine optimality guarantees at local optima, even when CQs do not hold. However, some second-order sequential optimality conditions still require some restrictive conditions on constraints in the recent literature. In this paper, we propose a new strong second-order sequential optimality condition without CQs. We also show that a penalty-type method and an augmented Lagrangian method generate points satisfying these new optimality conditions. |
| title | A strong second-order sequential optimality condition for nonlinear programming problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.01430 |