New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem
We study a nondifferentiable fractional programming problem as follows: (P)minx∈Kf(x)/g(x) subject to x∈K⊆X, hi(x)≤0, i=1,2,…,m, where K is a semiconnected subset in a locally convex topological vector space X, f:K→ℝ, g:K→ℝ+ and hi:K→ℝ, i=1,2,…, m. If f, -g, and hi, i=1,2,…,m, are arc-directional...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/527183 |
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| author | Yi-Chou Chen Wei-Shih Du |
| author_facet | Yi-Chou Chen Wei-Shih Du |
| author_sort | Yi-Chou Chen |
| collection | DOAJ |
| description | We study a nondifferentiable fractional programming problem as follows: (P)minx∈Kf(x)/g(x) subject to x∈K⊆X, hi(x)≤0, i=1,2,…,m, where K is a semiconnected subset in a locally convex topological vector space X, f:K→ℝ, g:K→ℝ+ and hi:K→ℝ, i=1,2,…, m. If f, -g, and hi, i=1,2,…,m, are arc-directionally differentiable, semipreinvex maps with respect to a continuous map γ:[0,1]→K⊆X satisfying γ(0)=0 and γ′(0+)∈K, then the necessary and sufficient conditions for optimality of (P) are established. |
| format | Article |
| id | doaj-art-9275ab8e45ef457a8dcd45ff779fa928 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9275ab8e45ef457a8dcd45ff779fa9282025-02-03T06:08:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/527183527183New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming ProblemYi-Chou Chen0Wei-Shih Du1Department of General Education, National Army Academy, Taoyuan 320, TaiwanDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, TaiwanWe study a nondifferentiable fractional programming problem as follows: (P)minx∈Kf(x)/g(x) subject to x∈K⊆X, hi(x)≤0, i=1,2,…,m, where K is a semiconnected subset in a locally convex topological vector space X, f:K→ℝ, g:K→ℝ+ and hi:K→ℝ, i=1,2,…, m. If f, -g, and hi, i=1,2,…,m, are arc-directionally differentiable, semipreinvex maps with respect to a continuous map γ:[0,1]→K⊆X satisfying γ(0)=0 and γ′(0+)∈K, then the necessary and sufficient conditions for optimality of (P) are established.http://dx.doi.org/10.1155/2013/527183 |
| spellingShingle | Yi-Chou Chen Wei-Shih Du New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem Journal of Applied Mathematics |
| title | New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem |
| title_full | New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem |
| title_fullStr | New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem |
| title_full_unstemmed | New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem |
| title_short | New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem |
| title_sort | new optimality conditions for a nondifferentiable fractional semipreinvex programming problem |
| url | http://dx.doi.org/10.1155/2013/527183 |
| work_keys_str_mv | AT yichouchen newoptimalityconditionsforanondifferentiablefractionalsemipreinvexprogrammingproblem AT weishihdu newoptimalityconditionsforanondifferentiablefractionalsemipreinvexprogrammingproblem |