Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints

• 成果类型: Article
• 署名作者: Hintermueller, Michael; Mordukhovich, Boris S.; Surowiec, Thomas M.
• 署名单位: Humboldt University of Berlin; Wayne State University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0704-6
• 发表日期: 2014
• 页码: 555-582
• 关键词: mathematical programs; complementarity constraints; optimality

摘要

The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and development of numerical methods. Though much can be said for broad classes of elliptic MPECs in both polyhedric and non-polyhedric settings, the calculation becomes significantly more complicated when additional constraints are imposed on the control. In this paper we develop three derivation methods for constrained MPEC problems: via concepts from variational analysis, via penalization of the control constraints, and via penalization of the lower-level problem with the subsequent regularization of the resulting nonsmoothness. The developed methods and obtained results are then compared and contrasted.