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在实赋范线性空间中利用锥方向高阶广义邻接导数研究带约束的集值优化在超有效解意义下的高阶Mond-Weir对偶问题.在广义锥-凸假设下,利用锥方向高阶广义邻接导数的性质借助凸集分离定理得到了强对偶定理.利用超有效点的标量化定理得到逆对偶定理. 相似文献
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讨论了集值优化问题严有效解的高阶导数型标量化定理.首先得到了集值优化问题严有效解的一个高阶导数型必要性条件,其次获得了集值优化问题严有效解的标量化必要性条件和充分性条件. 相似文献
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本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 . 相似文献
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一组三个函数乘积的高阶导数公式及其行列式表示 总被引:2,自引:0,他引:2
谭福锦 《数学的实践与认识》2006,36(7):372-378
研究了三个函数乘积的高阶导数,得到了一组相应的导数公式.利用这些公式求该类函数的高阶导数以及进行近似计算,或做函数的近似表示,将起到较好的简化作用. 相似文献
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本文应用陈怀惠和顾永兴关于Zalcman不正规性条件的改进结果,推广和加强了Lappan的一个正规定则,Lappan证明,若亚纯函数族中的所有函数的球面导数的害虫方(大于2)在紧集上的积发一致有界,则该族是有正则的,本文证明,把积分限制在函值数值模小于给常数的集上,结论仍然成立,同时,用高阶导数的积分替代球面导数的积分,得到十分一般的结果,另外对幂方为2的情形也进行了讨论。 相似文献
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In this paper, higher order generalized contingent epiderivative and higher order generalized adjacent epiderivative of set-valued maps are introduced. Necessary and sufficient conditions for Henig efficient solutions to a constrained set-valued optimization problem are given by employing the higher order generalized epiderivatives. 相似文献
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周志昂 《数学的实践与认识》2007,37(15):131-135
我们讨论了广义次似凸集值优化的对偶定理.首先,我们给出了广义次似凸集值优化的对偶问题.其次,我们给出了广义次似凸集值优化的对偶定理.最后,我们考虑了广义次似凸集值优化问题的标量化对偶,并给出了一系列对偶定理. 相似文献
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Euler数和高阶Euler数的推广 总被引:7,自引:0,他引:7
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended. 相似文献
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Gbor Sgi 《Mathematical Logic Quarterly》2002,48(2):261-275
Which ultraproducts preserve the validity of formulas of higher order logics? To answer this question, we will introduce natural topologies (which we call ultratopologies) on ultraproducts. We will show, that ultraproducts preserving certain higher order formulas can be characterized in terms of these topologies. As an application of the above results, we provide a constructive, purely model theoretic characterization for classes definable by second order existential formulas. 相似文献
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本文应用高阶微分不等式技巧和边界层校正法研究一类高阶非线性方程混合边值问题: e2yn=f(t,e,y,…,yn-2 Pj(ε)yj(0,ε)-qj(ε)yj+1(0,ε)=Aj(ε)(0≤j≤n-3)a1(ε)y(n-2)(0,ε)-a2(ε)yn-1(0,ε)=B(ε)b1(ε)y(n-2)(1,ε)十b2(ε)y(n-1)(1,ε)=C(ε)的奇异摄动。在较一般的条件下,证明了摄动解的存在性,并得到了摄动解直到n阶导函数的一致有效渐近展开式,从而推广和改进了前人的结果。 相似文献
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CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION 总被引:2,自引:0,他引:2
丘京辉 《数学物理学报(B辑英文版)》2007,27(1):211-218
By using cone-directed contingent derivatives, the unified necessary and suffi-cient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set valued optimization. 相似文献
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We introduce higher‐order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher‐order generalized invexity assumptions on functions that compose the primal problem, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter‐examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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In view of a new idea on initial conditions, an open problem of nonlinear evolution equations with higher order, which was given by J. L. Lions, is solved. Effect of our results is shown on an example. 相似文献