共查询到20条相似文献,搜索用时 89 毫秒
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借助于Ben-Tal广义代数运算引进了一种新的函数--- (h,φ)-Lipschitz函数. 讨论了它与Lipschitz函数之间的关系,给出了它的广义方向导数和广义梯度,得到了它们的若干性质. 作为应用,给出了广义方向导数与切锥之间的关系. 相似文献
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(h,ψ)-数学规划问题的必要条件 总被引:1,自引:0,他引:1
给出了(h,ψ)-η伪凸函数的概念,利用Ben-Tal广义代数运算讨论了它与η-伪凸函数之间的关系。当目标函数和约束函数均为(h,ψ)-可微函数时,在广义Slater约束规格下,得到了相应规划问题取得最优解的Kuhn-Tucker必要条件。 相似文献
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一类混合单调算子新的不动点定理及其应用 总被引:2,自引:0,他引:2
尹建东 《应用泛函分析学报》2009,11(3):268-273
引入了广义Φ凹(-φ)凸算子这一概念,在非紧非连续条件下,得到了混合单调算子的几个新的不动点存在唯一性定理.最后给出了一个应用. 相似文献
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广义度量S-KKM映射的性质及其对鞍点问题的应用 总被引:3,自引:0,他引:3
引入了S为集盥映射情况下的广义度量S-KKM映射和超S-γ-广义拟凸(凹)函数,建立了广义度量S-KKM映射原理和广义度量S-KKM映射与超S-γ-广义拟凸(凹)函数的关系.作为应用,获得了超凸度量空间中的新的Ky Fan极大极小不等式和鞍点定理. 相似文献
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童子双 《数学的实践与认识》2008,38(17)
对于一类目标函数中有无限个分式的广义分式规划,给出一个不完全Lagrange函数,并利用已有的最优性必要条件,在B-(p,r)-不变凸性的条件下,证明了鞍点最优性准则. 相似文献
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(h,φ)-不变广义凸函数的若干性质与(h,φ)-不变广义凸多目标规划的最优性及对偶性 总被引:8,自引:0,他引:8
研究了Ben-Tal广义代数运算的若干性质,引进了(h,φ)-不变广义凸函数的概念,讨论了(h,φ)-不变广义凸函数的若干性质,给出了(h,φ)-不变广义凸半无限多目标规划取得有效解(或弱有效解)的充分条件,建立了(h,φ)-不变广义凸多目标规划的Lagrange对偶理论。 相似文献
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近似锥一次类凸集值向量优化问题强有效解的广义鞍点刻画 总被引:1,自引:1,他引:0
本文研究了近似锥一次类凸集值向量优化强有效解的广义鞍点表示问题.利用择一定理,得到了近似锥-次类凸集值优化问题强有效解为广义鞍点的充分条件和必要条件.所得结果丰富了集值优化理论,并且拓广了广义鞍点的应用. 相似文献
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Vsevolod I. Ivanov 《Optimization Letters》2012,6(1):43-54
In this paper we define two notions: Kuhn–Tucker saddle point invex problem with inequality constraints and Mond–Weir weak
duality invex one. We prove that a problem is Kuhn–Tucker saddle point invex if and only if every point, which satisfies Kuhn–Tucker
optimality conditions forms together with the respective Lagrange multiplier a saddle point of the Lagrange function. We prove
that a problem is Mond–Weir weak duality invex if and only if weak duality holds between the problem and its Mond–Weir dual
one. Additionally, we obtain necessary and sufficient conditions, which ensure that strong duality holds between the problem
with inequality constraints and its Wolfe dual. Connections with previously defined invexity notions are discussed. 相似文献
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(p,r)-不变凸函数规划问题的鞍点定理 总被引:4,自引:0,他引:4
本文首先介绍了一个广义Lagrange向量函数L(x,u),并利用一类新的广义 凸函数:(p,r)——不变凸函数讨论了多目标分式规划问题的鞍点最优性条件. 相似文献
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《Optimization》2012,61(5):489-503
We introduce a notion of a second-order invex function. A Fréchet differentiable invex function without any further assumptions is second-order invex. It is shown that the inverse claim does not hold. A Fréchet differentiable function is second-order invex if and only if each second-order stationary point is a global minimizer. Two complete characterizations of these functions are derived. It is proved that a quasiconvex function is second-order invex if and only if it is second-order pseudoconvex. Further, we study the nonlinear programming problem with inequality constraints whose objective function is second-order invex. We introduce a notion of second-order type I objective and constraint functions. This class of problems strictly includes the type I invex ones. Then we extend a lot of sufficient optimality conditions with generalized convex functions to problems with second-order type I invex objective function and constraints. Additional optimality results, which concern type I and second-order type I invex data are obtained. An answer to the question when a kernel, which is not identically equal to zero, exists is given. 相似文献
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ON SUFFICIENCY AND DUALITY OF SOLUTIONS FOR QUASI Bs-INVEX SEMI-INFINITE PROGRAMMING 总被引:1,自引:0,他引:1
张庆祥 《高等学校计算数学学报(英文版)》2001,10(1)
1 IntroductionRecently,various kinds of generalized convex functions were introduced.Bector andSingh[1 ] introduced a class of functions which called B-vex function.Bector,Suneja,andLalitha[2 ] introduced quasi B-vex function,pseudo B-vex function,B-invex function,quasi B-invex function,and pseudo B-invex function.We[3] extended invex function[4] ,gave thedefinitions of the symmetricη-function,symmetricη-pseudoconvex function,symmetricη-quasiconvex function for symmetric differentiable… 相似文献
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Optimality criteria and duality in multiple-objective optimization involving generalized invexity 总被引:8,自引:0,他引:8
R. N. Kaul S. K. Suneja M. K. Srivastava 《Journal of Optimization Theory and Applications》1994,80(3):465-482
A multiple-objective optimization problem involving generalized invex functions is considered. Kuhn-Tucker type necessary and sufficient conditions are obtained for a feasible point to be an efficient or properly efficient solution. Two dual programs are obtained. The results are given under weaker invexity assumptions. 相似文献
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利用向量值广义凸函数等概念,讨论了一类不可微广义分布式规划的Lagrange函数,在适当条件下,证明了广义分式规划中的鞍点存在性定理。 相似文献
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群体多目标决策联合有效解类的不变凸充分条件 总被引:2,自引:0,他引:2
对于群体多目标决策问题,文[1]引进它的联合有效解类的概念,并给出这类解的最优性必要条件,在对于问题的目标函数和约束函数附加凸性的条件下,文[2]又给出了联合有效解类的最优性充分条件,本文进一步在目标函数和约束函数具不变凸和不变广义 凸的情况下,分别给出了联合有效解类的若干最优性充分条件。 相似文献
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REMARKS ON CRITERIA OF PREQUASI-INVEX FUNCTIONS 总被引:6,自引:0,他引:6
Luo Hezhi Wu Huixian Zhu Yihua Dept.of Math. Shanghai Univ. Shanghai China. Dept.of Appl.Math. Zhejiang Univ.of Technology Zhejiang China. College of Science Hangzhou Dianzi Univ. Zhejiang China. College of Business Administration Zhejiang Univ. of Technology Zhejiang China. 《高校应用数学学报(英文版)》2004,19(3):335-341
§1 IntroductionConvexity and generalized convexity play a central role in mathematical economics,engineering,managment science,and optimization theory.Therefore,the research onconvexity and generalized convexity is one of the most important aspects in mathematicalprogramming.Recently,[1] derived criteria for quasiconvex functions under lowersemicontinuity and upper semicontinuity conditions.In[2 ] Yang et al introduced variousconceptsof prequasi-invex functions,types ofgeneralized version o… 相似文献