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

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...

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Bibliographic Details
Published in:Mathematical programming Vol. 146; no. 1-2; pp. 555 - 582
Main Authors: Hintermüller, Michael, Mordukhovich, Boris S., Surowiec, Thomas M.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014
Springer Nature B.V
Subjects:
Analysis
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Constraints
Control theory
Convex analysis
Derivation
Equilibrium
Full Length Paper
Inequality
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Partial differential equations
Regularization
Studies
Theoretical
49K21
90C46
Stationarity conditions
Elliptic mathematical programs with equilibrium constraints
Control constraints
90C33
65K10
Optimal control of variational inequalities
Coderivatives
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0704-6