Sufficient Optimality Conditions in Bilevel Programming

• 成果类型: Article
• 署名作者: Mehlitz, Patrick; Zemkoho, Alain B.
• 署名单位: Brandenburg University of Technology Cottbus; University of Southampton
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1122
• 发表日期: 2021
• 页码: 1573-1598
• 关键词: mathematical programs; sensitivity-analysis; 2nd-order conditions; nonlinear programs; constraint; optimization; derivatives; uniqueness; calmness

摘要

This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by estimating the tangent cone to the feasible set of the bilevel program in terms of initial problem data. This is done by exploiting several different reformulations of the hierarchical model as a singlelevel problem. To obtain second-order sufficient optimality conditions, we exploit the socalled value function reformulation of the bilevel optimization problem, which is then tackled with the aid of second-order directional derivatives. The resulting conditions can be stated in terms of initial problem data in several interesting situations comprising the settings where the lower level is linear or possesses strongly stable solutions.