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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| Vydané v: | R.A.I.R.O. Recherche opérationnelle Ročník 56; číslo 3; s. 1397 - 1410 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
01.05.2022
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| ISSN: | 0399-0559, 2804-7303 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Iqbal, Akhlad Hussain, Askar |
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| Cites_doi | 10.33993/jnaat332-774 10.1155/2012/175176 10.1023/A:1021792726715 10.1186/s13660-015-0824-z 10.1016/0022-247X(81)90123-2 10.1080/09720502.2005.10700394 10.1023/A:1017532225395 10.1016/j.ejor.2007.11.056 10.1088/1757-899X/571/1/012025 10.1186/s13660-018-1944-z 10.1016/0165-0114(94)90011-6 10.1016/S0960-0779(00)00036-9 10.1080/01630563.2019.1651740 10.1016/j.na.2011.07.005 10.1016/0022-247X(88)90113-8 10.1017/S0334270000005142 10.1080/02331939108843693 10.1007/s10957-012-0052-3 10.1007/s12597-018-0346-9 10.1006/jmaa.1995.1057 10.1155/S0161171299225434 |
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| Snippet | 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... |
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| Title | Nonlinear programming problem for strongly E -invex sets and strongly E -preinvex functions |
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