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1.
本文考虑具有不等式约束条件不可微优化问题,假定目标函数和约束函数既是Lipschitz的也是拟可微的.证明了该问题拟微分形式下的FritzJohn点必是Clarke广义梯度形式下的FritzJohn点.另外,还给出了拟微分和Clarke广义梯度之间的关系. 相似文献
2.
借助于Ben—Tal广义代数运算引进了一种新的函数-(h,)-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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电动力学电磁场边值问题的广义变分原理 总被引:1,自引:0,他引:1
给出了线性各项异性电磁场边值问题的广义虚功原理表达式,运用钱伟长教授提出的方法建立了该问题的广义变分原理,可直接反映该问题的全部特征,即4个Maxwell方程、2个场强-位势方程、2个本构方程和8个边界条件.继而导出了一族有先决条件的广义变分原理.作为例证,导出了两个退化形式的广义变分原理,和已知的广义变分原理等价.此外还导出了两个修正的广义变分原理,可为该问题提供杂交有限元模型.建立的各广义变分原理可为电磁场边值问题的有限元应用提供更为完善的理论基础. 相似文献
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在非标准分析框架下,用离散函数定义新广义函数,用差商定义其导数.对Schwartz广义函数以及更广的Gevrey超广义函数,文章证明了广义导数可以用差商表示.此外还给出了此新广义函数和Sobolev理论的关系. 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
8.
讨论了不等式约束优化问题中拟微分形式下Fritz John必要条件与 Clarke广义梯度形式下Fritz John必要条件的关系.在较弱条件下给出了具有等式与不等式约束条件的两个Lagrange乘子形式的最优性必要条件,在这两个条件中等式约束函数的拟微分和Clarke广义梯度分别被使用。 相似文献
9.
广义G-M模型参数估计的一种相对效率 总被引:2,自引:0,他引:2
对于广义G—M模型,如果最小二乘估计(LSE)与最佳线性无偏估计(BLUE)相等,就可以用LSE代替BLUE反之,用LSE代替BLUE就要蒙受一些损失.有时,这种损失可能是很大的,因而研究这种损失的大小就显得颇为重要.本文提出了一种新的相对效率,并给出了该相对效率的上下界,最后讨论了该相对效率与广义相关系数的关系. 相似文献
10.
给出由非标准离散函数及其差商所定义的新广义函数的某些类,它们密切联系于通常的直至某阶为连续可微的函数.周的一个深刻的定理被用来建立这些类与非标准Sobolev空间之间的关系. 相似文献
11.
Clarke and Monzo defined in [3] a construction called a generalized inflation of a semigroup. It is always the case that any
inflation of a semigroup is a generalized inflation,
and any generalized inflation of a semigroup is a null extension of the semigroup. Clarke and Monzo proved that any associative
null extension of a base semigroup which is a union of
groups is in fact a generalized inflation. In this paper we study null extensions and generalized inflations of Brandt semigroups.
We first prove that any generalized inflation of a Brandt
semigroup is actually an inflation of the semigroup. This answers a question posed by Clarke and Monzo in [3]. Then we characterize
associative null extensions of Brandt semigroups, and show that there are associative null extensions of Brandt semigroups
which are not generalized inflations. 相似文献
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The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation oil its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat. 相似文献
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It is shown that any generalized Jordan (triple-)derivation on a 2–torsion free semiprime ring is a generalized derivation
and that any generalized Jordan higher derivation on a 2–torsion free semiprime ring is a generalized higher derivation. Then
we give several conditions which enable some generalized Jordan derivations on prime rings to degenerate left or right multipliers.
Lastly, we apply these degenerating conditions to discuss the range inclusion problems of generalized derivations on noncommutative
Banach algebras. 相似文献
16.
Yu. G. Rykov 《Proceedings of the Steklov Institute of Mathematics》2018,301(1):213-227
The paper contains results concerning the development of a new approach to the proof of existence theorems for generalized solutions to systems of quasilinear conservation laws. This approach is based on reducing the search for a generalized solution to analyzing extremal properties of a certain set of functionals and is referred to as a variational approach. The definition of a generalized solution can be naturally reformulated in terms of the existence of critical points for a set of functionals, which is convenient within the approach proposed. The variational representation of generalized solutions, which was earlier known for Hopf-type equations, is generalized to systems of quasilinear conservation laws. The extremal properties of the functionals corresponding to systems of conservation laws are described within the variational approach, and a strategy for proving the existence theorem is outlined. In conclusion, it is shown that the variational approach can be generalized to the two-dimensional case. 相似文献
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Dijana Mosi? 《Applied mathematics and computation》2009,215(8):2826-2834
In this paper we obtain the formula for computing the condition number of a complex matrix, which is related to the outer generalized inverse of a given matrix. We use the Schur decomposition of a matrix. We characterize the spectral norm and the Frobenius norm of the relative condition number of the generalized inverse, and the level-2 condition number of the generalized inverse. The sensitivity for the generalized Drazin-inverse solution of linear systems is presented. We also present the structured perturbation of the generalized inverse. 相似文献
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S. Karamardian S. Schaible J. P. Crouzeix 《Journal of Optimization Theory and Applications》1993,76(3):399-413
This paper is a sequel to Ref. 1 in which several kinds of generalized monotonicity were introduced for maps. They were related to generalized convexity properties of functions in the case of gradient maps. In the present paper, we derive first-order characterizations of generalized monotone maps based on a geometrical analysis of generalized monotonicity. These conditions are both necessary and sufficient for generalized monotonicity. Specialized results are obtained for the affine case. 相似文献
19.
Augusto Ferrante 《Linear and Multilinear Algebra》2013,61(11):1460-1474
This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati equation. In particular, an analysis on the eigenstructure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalized discrete algebraic Riccati equation are coincident. This subspace is the key to derive a decomposition technique for the generalized Riccati difference equation. This decomposition isolates a “nilpotent” part, which converges to a steady-state solution in a finite number of steps, from another part that can be computed by iterating a reduced-order generalized Riccati difference equation. 相似文献
20.
We solve a generalized Gauss problem in the Euclidean plane which states that: Given a convex quadrilateral, a positive number (weight) that corresponds to each of its vertices and a length of a linear segment which connects two mobile interior points of the quadrilateral find the minimum weighted network, which connects two of the vertices with one interior point and the other two with another interior point (Generalized Gauss tree). Furthermore, we introduce a generalized Gauss variable which corresponds to the unknown weight of the given distance which connects the two mobile interior points and obtain a degenerate generalized Gauss tree which corresponds to a specific value of the generalized Gauss variable that minimizes the length of the induced generalized Gauss trees and the weighted Fermat–Torricelli tree for a specific value of the generalized Gauss variable that maximizes the length of the induced generalized Gauss trees. Following this technique, we introduce a new class of generalized Gauss trees that we call absorbing generalized Gauss trees and a new class of Fermat–Torricelli trees that we call absorbing Fermat–Torricelli trees with respect to the sum of the four given weights of the convex quadrilateral. 相似文献