Abstract
Necessary conditions for the optimality of a pair (y*, u*) with respect to the cost functional g(y) + h(u) subject to Ay∋Bu + f are given in terms of generalized gradients. Here, g is locally Lipschitz, h is convex, A is a maximal strongly monotone operator, and B is linear. Two examples of applications of our necessary conditions to nonlinear partial differential equations of elliptic type are presented.
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