| Title:
|
Saddle point criteria for second order $\eta $-approximated vector optimization problems (English) |
| Author:
|
Jayswal, Anurag |
| Author:
|
Jha, Shalini |
| Author:
|
Choudhury, Sarita |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
359-378 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to apply second order $\eta$-approximation method introduced to optimization theory by Antczak [2] to obtain a new second order $\eta$-saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order $\eta$-saddle point and the second order $\eta$-Lagrange function are defined for the second order $\eta$-approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the considered vector optimization problem and a second order $\eta$-saddle point of the second order $\eta$-Lagrangian in the associated second order $\eta$-approximated vector optimization problem is established under the assumption of second order invexity. (English) |
| Keyword:
|
efficient solution |
| Keyword:
|
second order $\eta $-approximation |
| Keyword:
|
saddle point criteria |
| Keyword:
|
optimality condition |
| MSC:
|
90C26 |
| MSC:
|
90C29 |
| MSC:
|
90C30 |
| MSC:
|
90C46 |
| idZBL:
|
Zbl 06644300 |
| idMR:
|
MR3532512 |
| DOI:
|
10.14736/kyb-2016-3-0359 |
| . |
| Date available:
|
2016-07-17T12:13:27Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145781 |
| . |
| Reference:
|
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| Reference:
|
[2] Antczak, T.: An $\eta$-approximation method in nonlinear vector optimization..Nonlinear Anal. 63 (2005), 225-236. Zbl 1093.90053, MR 2165497, 10.1023/a:1021834210437 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
