| Title:
|
A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions (English) |
| Author:
|
Antczak, Tadeusz |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
5 |
| Year:
|
2009 |
| Pages:
|
433-445 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order $\eta $-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order $\eta $-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order $\eta $-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem. (English) |
| Keyword:
|
mathematical programming |
| Keyword:
|
second order $\eta $-approximated optimization problem |
| Keyword:
|
second order invex function |
| Keyword:
|
second order optimality conditions |
| MSC:
|
52A01 |
| MSC:
|
90C26 |
| MSC:
|
90C30 |
| MSC:
|
90C46 |
| idZBL:
|
Zbl 1212.90307 |
| idMR:
|
MR2545410 |
| DOI:
|
10.1007/s10492-009-0028-2 |
| . |
| Date available:
|
2010-07-20T13:20:49Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140377 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Bector, C. R., Bector, B. K.: (Generalized)-bonvex functions and second order duality for a nonlinear programming problem.Congr. Numerantium 52 (1985), 37-52. |
| 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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| . |
