Several Approaches for the Derivation of Stationarity Conditions for Elliptic MPECs with Upper-Level Control Constraints
Please always quote using this URN:urn:nbn:de:0296-matheon-8775
- The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and de- velopment 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 com- plicated 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.
Author: | Michael Hintermüller, Boris S. Mordukhovich, Thomas Surowiec |
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URN: | urn:nbn:de:0296-matheon-8775 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/08/09 |
Release Date: | 2011/08/09 |
Tag: | elliptic MPEC; variational analysis |
Institute: | Humboldt-Universität zu Berlin |
MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K21 Problems involving relations other than differential equations |
Preprint Number: | 811 |