Optimization problems with equilibrium constraints and their numerical solution

• 成果类型: Article; Proceedings Paper
• 署名作者: Kocvara, M; Outrata, JV
• 署名单位: University of Erlangen Nuremberg; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-004-0539-2
• 发表日期: 2004
• 页码: 119-149
• 关键词: interior-point algorithm; mathematical programs; exact penalization; complementarity constraints; optimality conditions; nonsmooth; stationarity; version

摘要

We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (Mathematical Programs with Equilibrium Constraints) and MPCC (Mathematical Programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach (ImP). We further present a new theoretical framework for the ImP technique that is particularly useful in case of difficult equilibria. Finally, three numerical examples are presented: an MPEC that can be solved by ImP but can hardly be formulated as a nonlinear program, an MPCC that cannot be solved by ImP and finally an MPEC solvable by both, ImP and NLP techniques. In the last example we compare the efficiency of the two approaches.