# On necessary optimality conditions in a class of optimization problems

Aplikace matematiky (1989)

- Volume: 34, Issue: 6, page 466-474
- ISSN: 0862-7940

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topOutrata, Jiří V.. "On necessary optimality conditions in a class of optimization problems." Aplikace matematiky 34.6 (1989): 466-474. <http://eudml.org/doc/15602>.

@article{Outrata1989,

abstract = {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.},

author = {Outrata, Jiří V.},

journal = {Aplikace matematiky},

keywords = {Clarke regular graph; necessary conditions; tangent cone; locally Lipschitz objective function; set-valued map; Clarke normal cone; generalized gradient; contingent cone; Clarke regular graph; necessary conditions; tangent cone; locally Lipschitz objective function; set-valued map; Clarke normal cone; generalized gradient; contingent cone},

language = {eng},

number = {6},

pages = {466-474},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On necessary optimality conditions in a class of optimization problems},

url = {http://eudml.org/doc/15602},

volume = {34},

year = {1989},

}

TY - JOUR

AU - Outrata, Jiří V.

TI - On necessary optimality conditions in a class of optimization problems

JO - Aplikace matematiky

PY - 1989

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 34

IS - 6

SP - 466

EP - 474

AB - 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.

LA - eng

KW - Clarke regular graph; necessary conditions; tangent cone; locally Lipschitz objective function; set-valued map; Clarke normal cone; generalized gradient; contingent cone; Clarke regular graph; necessary conditions; tangent cone; locally Lipschitz objective function; set-valued map; Clarke normal cone; generalized gradient; contingent cone

UR - http://eudml.org/doc/15602

ER -

## References

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