A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming
A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/629194 |
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| _version_ | 1849304723838992384 |
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| author | Hehua Jiao Sanyang Liu Xinying Pai |
| author_facet | Hehua Jiao Sanyang Liu Xinying Pai |
| author_sort | Hehua Jiao |
| collection | DOAJ |
| description | A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming. |
| format | Article |
| id | doaj-art-3aee28e2d7cc4dfea6341dadc95ddab0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3aee28e2d7cc4dfea6341dadc95ddab02025-08-20T03:55:40ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/629194629194A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear ProgrammingHehua Jiao0Sanyang Liu1Xinying Pai2College of Science, Xidian University, Xi'an, Shanxi 710071, ChinaCollege of Science, Xidian University, Xi'an, Shanxi 710071, ChinaCollege of Science, Xidian University, Xi'an, Shanxi 710071, ChinaA kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.http://dx.doi.org/10.1155/2012/629194 |
| spellingShingle | Hehua Jiao Sanyang Liu Xinying Pai A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming Journal of Applied Mathematics |
| title | A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming |
| title_full | A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming |
| title_fullStr | A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming |
| title_full_unstemmed | A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming |
| title_short | A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming |
| title_sort | class of semilocal e preinvex functions and its applications in nonlinear programming |
| url | http://dx.doi.org/10.1155/2012/629194 |
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