共查询到17条相似文献,搜索用时 63 毫秒
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关于E-凸函数及E-凸规划几个错误结论的修正 总被引:2,自引:0,他引:2
本文研究Youness在1999年建立的有关E凸函数和E规划的结论.利用E凸函数和E凸规划的基本性质和优化分析技术,获得了有关E凸函数E凸规划的几个错误结论的修正.. 相似文献
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旷华武 《数学的实践与认识》2019,(4)
研究十二类广义凸函数相关集合的对称性问题及其对应函数的中点凸性问题.证明了其中的十个集合具有对称性,应用反例说明了余下的两个集合不必具有对称性.证明了六个集合对应的函数具有中点凸性,应用反例说明了余下六个集合对应的函数不必具有中点凸性. 相似文献
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在更弱的连续假设下研究集合A_(x,y)={λ∈[0,1]|f(λE(x)+(1-λ)E(y))≤λf(E(x))+(1-λ)f(E(y))}和集合A′_(x,y)={λ∈[0,1]|f(λE(x)+(1-λ)E(y))≤max{f(E(x)),f(E(y))}}的稠密性、闭性、(弱)近似凸性,得到E-凸函数和E-拟凸函数的等价条件. 相似文献
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研究了广义凸Fuzzy集和广义反凸Fuzzy集以及它们的性质。通过将凸Fuzzy集和E-凸集相结合,提出了一种新的广义凸Fuzzy集———E-凸Fuzzy集,使得凸Fuzzy集成为它的特例,并对E-凸Fuzzy集的性质进行了初步研究。然后,类似地,通过将反凸Fuzzy集和E-凸集相结合,提出了一种新的广义反凸Fuzzy集———E-反凸Fuzzy集,使得反凸Fuzzy集成为它的特例,并对E-反凸Fuzzy集的性质进行了初步研究。 相似文献
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应用新方法,研究十二类广义凸函数相关集合的稠密性问题.证明了其中的八个集合在[0,1]中是稠密的.应用反例说明了其中的四个集合在[0,1]中不必稠密. 相似文献
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E-Convex Sets, E-Convex Functions, and E-Convex Programming 总被引:34,自引:0,他引:34
E. A. Youness 《Journal of Optimization Theory and Applications》1999,102(2):439-450
A class of sets and a class of functions called E-convex sets and E-convex functions are introduced by relaxing the definitions of convex sets and convex functions. This kind of generalized convexity is based on the effect of an operator E on the sets and domain of definition of the functions. The optimality results for E-convex programming problems are established. 相似文献
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On E-Convex Sets, E-Convex Functions, and E-Convex Programming 总被引:15,自引:0,他引:15
X. M. Yang 《Journal of Optimization Theory and Applications》2001,109(3):699-704
Recently, E-convex sets and E-convex functions were introduced in Ref. 1. However, some results seem to be incorrect. In this note, some counterexamples are given. 相似文献
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具有(F,α,ρ,d)—凸的分式规划问题的最优性条件和对偶性 总被引:1,自引:0,他引:1
给出了一类非线性分式规划问题的参数形式和非参数形式的最优性条件,在此基础上,构造出了一个参数对偶模型和一个非参数对偶模型,并分别证明了其相应的对偶定理,这些结果是建立在次线性函数和广义凸函数的基础上的. 相似文献
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Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems 总被引:25,自引:0,他引:25
Liang Z. A. Huang H. X. Pardalos P. M. 《Journal of Optimization Theory and Applications》2001,110(3):611-619
In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions. 相似文献
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具有(F α,ρ,d)-V-凸的非光滑多目标分式规划的最优性条件和对偶性 总被引:1,自引:0,他引:1
本文考虑了一类非光滑多目标分式规划问题,该多目标分式规划问题中所出现的函数是局部Lipschitz的.对该类多目标分式规划问题,引入了(F,α,ρ,d)-V-凸函数的概念,证明了有效解的充分条件和必要条件,构造出了一种参数对偶模型和一种半参数对偶模型,并证明了相应的对偶定理. 相似文献
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A New Self-Dual Embedding Method for Convex Programming 总被引:5,自引:0,他引:5
Shuzhong Zhang 《Journal of Global Optimization》2004,29(4):479-496
In this paper we introduce a conic optimization formulation to solve constrained convex programming, and propose a self-dual embedding model for solving the resulting conic optimization problem. The primal and dual cones in this formulation are characterized by the original constraint functions and their corresponding conjugate functions respectively. Hence they are completely symmetric. This allows for a standard primal-dual path following approach for solving the embedded problem. Moreover, there are two immediate logarithmic barrier functions for the primal and dual cones. We show that these two logarithmic barrier functions are conjugate to each other. The explicit form of the conjugate functions are in fact not required to be known in the algorithm. An advantage of the new approach is that there is no need to assume an initial feasible solution to start with. To guarantee the polynomiality of the path-following procedure, we may apply the self-concordant barrier theory of Nesterov and Nemirovski. For this purpose, as one application, we prove that the barrier functions constructed this way are indeed self-concordant when the original constraint functions are convex and quadratic. We pose as an open question to find general conditions under which the constructed barrier functions are self-concordant. 相似文献
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For a multiobjective bilevel programming problem(P) with an extremal-value function,its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved.Under some convexity and monotonicity assumptions,the weak and strong duality assertions are obtained. 相似文献