| Title:
|
Vector Optimization Results for $\ell $-Stable Data (English) |
| Author:
|
Dvorská, Marie |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
43-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to summarize basic facts about $\ell $-stable at a point vector functions and existing results for certain vector constrained programming problem with $\ell$-stable data. (English) |
| Keyword:
|
$\ell$-stable function |
| Keyword:
|
generalized second-order directional derivative |
| Keyword:
|
Dini derivative |
| Keyword:
|
weakly efficient minimizer |
| Keyword:
|
isolated minimizer |
| MSC:
|
49J50 |
| MSC:
|
49J52 |
| MSC:
|
49K10 |
| MSC:
|
90C29 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 1287.49016 |
| idMR:
|
MR3202378 |
| . |
| Date available:
|
2013-12-18T15:21:30Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143537 |
| . |
| Reference:
|
[1] Bednařík, D., Pastor, K.: On second-order conditions in unconstrained optimization. Math. Program. (Ser. A) 113, 2 (2008), 283–298. Zbl 1211.90276, MR 2375484, 10.1007/s10107-007-0094-8 |
| Reference:
|
[2] Bednařík, D., Pastor, K.: Decrease of $C^{1,1}$ property in vector optimization. RAIRO-Operations Research 43 (2009), 359–372. Zbl 1193.49016, MR 2573992, 10.1051/ro/2009023 |
| Reference:
|
[3] Bednařík, D., Pastor, K.: On second-order condition in constrained vector optimization. Nonlinear Analysis 74 (2011), 1372–1382. MR 2746815, 10.1016/j.na.2010.10.009 |
| Reference:
|
[4] Bednařík, D., Pastor, K.: Composition of $\ell$-stable vector functions. Mathematica Slovaca 62 (2012), 995–1005. MR 2981835, 10.2478/s12175-012-0060-7 |
| Reference:
|
[5] Dvorská, M., Pastor, K.: On comparison of $\ell$-stable vector optimization results. Mathematica Slovaca, in print. |
| Reference:
|
[6] Ginchev I.: On scalar and vector $\ell $-stable functions. Nonlinear Analysis 74 (2011), 182–194. Zbl 1205.26007, MR 2734988, 10.1016/j.na.2010.08.032 |
| Reference:
|
[7] Ginchev, I., Guerraggio, A.: Second-order conditions for constrained vector optimization problems with $\ell$-stable data. Optimization 60 (2011), 179–199. Zbl 1237.90221, MR 2772143, 10.1080/02331930903578718 |
| Reference:
|
[8] Ginchev, I., Guerraggio, A., Rocca, M.: From scalar to vector optimization. Applications of Mathematics 51 (2006), 5–36. Zbl 1164.90399, MR 2197320, 10.1007/s10492-006-0002-1 |
| Reference:
|
[9] Jahn J.: Vector optimization. Springer-Verlag, Berlin, 2004. Zbl 1055.90065, MR 2058695 |
| Reference:
|
[10] Khanh, P. Q., Tuan, N. D.: Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives. J. Optim. Theory Appl. 133 (2007), 341–357. Zbl 1149.90134, MR 2333819, 10.1007/s10957-007-9169-1 |
| . |
