TY - GEN A1 - Hintermüller, Michael A1 - Surowiec, Thomas T1 - First Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis N2 - 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. KW - Elliptic MPEC KW - Variational Inequality KW - Contingent Derivative KW - Epiconvergence KW - Epiderivative KW - Strong Stationarity KW - Pointwise Gradient Constraints Y1 - 2010 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/701 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-7019 ER -