Geodesic
On necessary optimality conditions in a class of optimization problems
Applications of Mathematics, Tome 34 (1989) no. 6, pp. 466-474.

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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.
DOI : 10.21136/AM.1989.104377
Classification : 49B34, 49J52, 49K27, 49K99, 90C30, 90C99
Keywords: Clarke regular graph; necessary conditions; tangent cone; locally Lipschitz objective function; set-valued map; Clarke normal cone; generalized gradient; contingent cone 
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     title = {On necessary optimality conditions in a class of optimization problems},
     journal = {Applications of Mathematics},
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Outrata, Jiří V. On necessary optimality conditions in a class of optimization problems. Applications of Mathematics, Tome 34 (1989) no. 6, pp. 466-474. doi : 10.21136/AM.1989.104377. http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104377/

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