A strong second-order sequential optimality condition for nonlinear programming problems

Fuente: arXiv
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Main Authors: Li, Huimin, Yamakawa, Yuya, Fukuda, Ellen H., Yamashita, Nobuo
Format: Preprint
Published: 2025
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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