| Title:
|
On necessary optimality conditions in a class of optimization problems (English) |
| Author:
|
Outrata, Jiří V. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
6 |
| Year:
|
1989 |
| Pages:
|
466-474 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Clarke regular graph |
| Keyword:
|
necessary conditions |
| Keyword:
|
tangent cone |
| Keyword:
|
locally Lipschitz objective function |
| Keyword:
|
set-valued map |
| Keyword:
|
Clarke normal cone |
| Keyword:
|
generalized gradient |
| Keyword:
|
contingent cone |
| MSC:
|
49B34 |
| MSC:
|
49J52 |
| MSC:
|
49K27 |
| MSC:
|
49K99 |
| MSC:
|
90C30 |
| MSC:
|
90C99 |
| idZBL:
|
Zbl 0699.90082 |
| idMR:
|
MR1026511 |
| DOI:
|
10.21136/AM.1989.104377 |
| . |
| Date available:
|
2008-05-20T18:37:59Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104377 |
| . |
| Reference:
|
[1] J.-P. Aubin I. Ekeland: Applied Nonlinear Analysis.Wiley, New York 1984. MR 0749753 |
| Reference:
|
[2] J. M. Borwein: Multivalued convexity: a unified approach to equality and inequality constraints.Math. Programming 13 (1977), 163-180. |
| Reference:
|
[3] F. H. Clarke: Optimization and Nonsmooth Analysis.Wiley, New York 1983. Zbl 0582.49001, MR 0709590 |
| Reference:
|
[4] P. H. Dien P. H. Sach: Further properties of the regularity of inclusion systems.Preprint 87-21, Inst. of Mathematics, Hanoi 1987. |
| Reference:
|
[5] J.-В. Hiriart-Urruty: Gradients generalisés de fonctions marginales.SIAM J. Control Optim. 16(1978), 301-316. Zbl 0385.90099, MR 0493610, 10.1137/0316019 |
| Reference:
|
[6] A. D. Ioffe: Necessary and sufficient conditions for a local minimum. Part 1: A reduction theorem and first order conditions.SIAM J. Control Optim. 17 (1979), 245-250. MR 0525025, 10.1137/0317019 |
| Reference:
|
[7] B. N. Pschenichnyi: Convex set-valued mappings and their adjoints.Kibernetika 3 (1972), 94-102 (in Russian). |
| Reference:
|
[8] B. N. Pschenichnyi: Convex Analysis and Extremal Problems.Nauka, Moscow 1982 (in Russian). |
| Reference:
|
[9] S. M. Robinson: Generalized equations and their solutions. Part II: Applications to nonlinear programming.Univ. Wisconsin-Madison, Technical Summary Rep. # 2048, 1980. |
| Reference:
|
[10] R. T. Rockafellar: Directional differentiability of the optimal value function in a nonlinear programming problem.Math. Prog. Study 21 (1984), 213-226. Zbl 0546.90088, MR 0751251, 10.1007/BFb0121219 |
| Reference:
|
[11] P. H. Sach: Regularity, calmness and support principle.Optimization 19 (1988), 13 - 27. Zbl 0648.49016, MR 0926215, 10.1080/02331938808843311 |
| . |
