Simple bilevel programming and extensions

• 成果类型: Article
• 署名作者: Dempe, Stephan; Nguyen Dinh; Dutta, Joydeep; Pandit, Tanushree
• 署名单位: Technical University Freiberg; Vietnam National University Ho Chi Minh City (VNUHCM) System; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01509-x
• 发表日期: 2021
• 页码: 227-253
• 关键词: constraint qualification; convex; optimality

摘要

In this paper we discuss the simple bilevel programming problem (SBP) and its extension, the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their interrelations. Next we study the various types of necessary and sufficient optimality conditions for the (SMPEC) problems, which occur under various reformulations. The optimality conditions for (SBP) are special cases of the results obtained for (SMPEC) when the lower level objective is the gradient of a convex function. Among the various optimality conditions presented in this article are the sequential optimality conditions, which do not need any constraint qualification. We also present a schematic algorithm for (SMPEC), where the sequential optimality conditions play a key role in the convergence analysis.