• search hit 3 of 6
Back to Result List

First Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis

Please always quote using this URN:urn:nbn:de:0296-matheon-7019
  • Mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality, so-called ``elliptic MPECs'', are formulated in reflexive Banach spaces. With the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures, variational analytic concepts are both applied and further developed. The paper is split into two main parts. The first part concerns the derivation of conditions in which the state constraints are assumed to be polyhedric sets. This part is then completed by two examples, the latter of which involves pointwise bilateral bounds on the gradient of the state. The second part begins with the derivation of a formula for the second order (Mosco) epiderivative of the indicator function of a general convex set. This result is then used to derive analogous conditions to those which are presented in the first part. Finally, an elliptic MPEC is considered important to the study of elasto-plasticity in which the pointwise Euclidean norm of the gradient of the state is bounded. Explicit strong stationarity conditions are provided for this problem.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Michael Hintermüller, Thomas Surowiec
URN:urn:nbn:de:0296-matheon-7019
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/07/16
Release Date:2010/07/16
Tag:
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J53 Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K10 Optimization and variational techniques [See also 49Mxx, 93B40]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions)
Preprint Number:710
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.