In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints $x \in S, 0 \in F(x)$, where $S$ is a closed set and $F$ is a set-valued map. No convexity requirements are imposed on $F$. The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.
@article{104377, author = {Ji\v r\'\i\ V. Outrata}, title = {On necessary optimality conditions in a class of optimization problems}, journal = {Applications of Mathematics}, volume = {34}, year = {1989}, pages = {466-474}, zbl = {0699.90082}, mrnumber = {1026511}, language = {en}, url = {http://dml.mathdoc.fr/item/104377} }
Outrata, Jiří V. On necessary optimality conditions in a class of optimization problems. Applications of Mathematics, Tome 34 (1989) pp. 466-474. http://gdmltest.u-ga.fr/item/104377/
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