Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem
This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimalit...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9849636 |
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| author | Wenyan Han Guolin Yu Tiantian Gong |
| author_facet | Wenyan Han Guolin Yu Tiantian Gong |
| author_sort | Wenyan Han |
| collection | DOAJ |
| description | This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established. |
| format | Article |
| id | doaj-art-57214555ff054f53a5517e5c00223352 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-57214555ff054f53a5517e5c002233522025-02-03T06:05:18ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/98496369849636Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming ProblemWenyan Han0Guolin Yu1Tiantian Gong2Institute of Applied Mathematics, North Minzu University, Yinchuan 750021, ChinaInstitute of Applied Mathematics, North Minzu University, Yinchuan 750021, ChinaInstitute of Applied Mathematics, North Minzu University, Yinchuan 750021, ChinaThis note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established.http://dx.doi.org/10.1155/2020/9849636 |
| spellingShingle | Wenyan Han Guolin Yu Tiantian Gong Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem Complexity |
| title | Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem |
| title_full | Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem |
| title_fullStr | Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem |
| title_full_unstemmed | Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem |
| title_short | Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem |
| title_sort | optimality conditions for a nonsmooth uncertain multiobjective programming problem |
| url | http://dx.doi.org/10.1155/2020/9849636 |
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