| 半(p,r)-不变凸多目标分式规划的Wolfe型对偶 |
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| 引用本文： | 焦合华. 半(p,r)-不变凸多目标分式规划的Wolfe型对偶[J]. 四川师范大学学报(自然科学版), 2011, 34(5): 659-662. DOI: 10.3969/j.issn.1001-8395.2011.05.013 |
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| 作者姓名： | 焦合华 |
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| 作者单位： | 长江师范学院数学与计算机学院,重庆,408100 |
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| 基金项目： | 国家自然科学基金(10471159);重庆市教委科学技术研究基金(KJ071305)资助项目 |
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| 摘 要： | 半(p,r)-不变凸函数是一类新的广义凸函数,它既是半预不变凸函数,又是(p,r)-预不变凸函数的真推广,从而是熟知的凸函数和不变凸函数的推广形式.首先,利用了一个广义Lagrange向量函数L(x,u),建立了多目标分式规划问题的Wolfe型对偶(FD).接着,在半(p,r)-不变凸性条件下,得到了几个弱对偶、强对偶和严格逆对偶定理.其结论具有一般性,推广了许多涉及凸函数、不变凸函数、半预不变凸函数和(p,r)-(预)不变凸函数的文献的结论.
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| 关 键 词： | 半p-不变凸集 半(p,r)-不变凸函数 多目标分式规划 Wolfe型对偶 |
Wolfe Duality for Multiobjective Fractional Programming with Semi(p,r)-Invexity Functions |
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| JIAO He-hua. Wolfe Duality for Multiobjective Fractional Programming with Semi(p,r)-Invexity Functions[J]. Journal of Sichuan Normal University(Natural Science), 2011, 34(5): 659-662. DOI: 10.3969/j.issn.1001-8395.2011.05.013 |
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| Authors: | JIAO He-hua |
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| Affiliation: | JIAO He-hua(College of Mathematics and Computer,Yangtze Normal College,Chongqing 408100) |
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| Abstract: | Semi(p,r)-invexity functions are new generalized invex functions.They are real generalization of the semi preinvexity functions and(p,r)-preinvexity functions,thus they are the generalization of well known convexity functions and invexity functions.First,by using a generalized Lagrange vector function L(x,u),the Wolfe dual(FD) of the multiobjective fractional programming problems is established.Second,some weak,strong and strict converse duality theorems are derived under semi(p,r)-invexity assumptions.The work generalizes many results on programming problems with convex functions,invex functions,semipreinvexity functions and(p,r)-(pre)invexity functions. |
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| Keywords: | semi p-invex set semi(p,r)-invexity functions multiobjective fractional programming Wolfe duality |
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