Nonlinear programming problem for strongly E -invex sets and strongly E -preinvex functions
The concepts of strongly E -invex sets, strongly E -invex, strongly E -preinvex, and strongly pseudo E -preinvex functions are introduced in this paper. We have included several non-trivial examples to support our definitions. The family of strongly E -invex sets has been shown to form a vector spac...
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| Published in: | R.A.I.R.O. Recherche opérationnelle Vol. 56; no. 3; pp. 1397 - 1410 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.05.2022
|
| ISSN: | 0399-0559, 2804-7303 |
| Online Access: | Get full text |
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| Summary: | The concepts of strongly
E
-invex sets, strongly
E
-invex, strongly
E
-preinvex, and strongly pseudo
E
-preinvex functions are introduced in this paper. We have included several non-trivial examples to support our definitions. The family of strongly
E
-invex sets has been shown to form a vector space over
R
, and other interesting properties have been addressed. The epigraph of strongly
E
-preinvex function has been derived, as well as the relationship between the strongly
E
-preinvex function and the strongly pseudo
E
-preinvex function has been established. To show an important relationship between strongly
E
-invex and strongly
E
-preinvex functions, a new Condition A has been introduced. A nonlinear programming problem for strongly
E
-preinvex functions is explored as an application. Under a few conditions, it has been proved that the local minimum point is the global minimum for a nonlinear programming problem. |
|---|---|
| ISSN: | 0399-0559 2804-7303 |
| DOI: | 10.1051/ro/2022064 |