التفاصيل البيبلوغرافية
| العنوان: |
New second-order optimality conditions for directional optimality of a general set-constrained optimization problem |
| المؤلفون: |
Ouyang, Wei, Ye, Jane, Zhang, Binbin |
| سنة النشر: |
2024 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Optimization and Control |
| الوصف: |
In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a directional neighborhood) in pursuit of developing these new optimality conditions. First-order necessary conditions for local optimality in given directions are provided by virtue of the corresponding directional normal cones. Utilizing the classical and/or the lower generalized support function, we obtain new second-order necessary and sufficient conditions for local optimality of general nonconvex constrained optimization problem in given directions via both the corresponding asymptotic second-order tangent cone and outer second-order tangent set. Our results do not require convexity and/or nonemptyness of the outer second-order tangent set. This is an important improvement to other results in the literature since the outer second-order tangent set can be nonconvex and empty even when the set is convex. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2404.17696 |
| رقم الانضمام: |
edsarx.2404.17696 |
| قاعدة البيانات: |
arXiv |