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991.
在[1]中,Solodov将非线性互补问题等价地转化成一个带非负约束的优化问题.基于这种转化形式,我们给出了一种求解非线性互补问题的下降算法.在映射为强单调时,证明了算法的全局收敛性. 相似文献
992.
Stefan M. Stefanov 《Computational Optimization and Applications》2001,18(1):27-48
A minimization problem with convex and separable objective function subject to a separable convex inequality constraint and bounded variables is considered. A necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. Convex minimization problems subject to linear equality/linear inequality constraint, and bounds on the variables are also considered. A necessary and sufficient condition and a sufficient condition, respectively, are proved for a feasible solution to be an optimal solution to these two problems. Algorithms of polynomial complexity for solving the three problems are suggested and their convergence is proved. Some important forms of convex functions and computational results are given in the Appendix. 相似文献
993.
Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints 总被引:2,自引:0,他引:2
Jean-Baptiste Hiriart-Urruty 《Journal of Global Optimization》2001,21(4):443-453
For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of -subdifferentials of convex functions and -normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality. 相似文献
994.
Akira Hiraki 《Journal of Algebraic Combinatorics》2001,14(2):127-131
Let be a distance-regular graph of diameter d, valency k and r := maxi | (c
i,b
i) = (c
1,b
1). Let q be an integer with r + 1 q d – 1.In this paper we prove the following results:
Theorem 1
Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 i q
and for any pair of vertices at distance i there exists a strongly closed subgraph of diameter i containing them.
Theorem 2
If r 2, then
c
2r+3 1.As a corollary of Theorem 2 we have d k
2(r + 1) if r 2. 相似文献
995.
Christian Zillober 《Numerical Algorithms》2001,27(3):265-289
The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the methods are extended for a general mathematical programming framework and a new scheme to update certain penalty parameters is defined, which leads to a considerable improvement in the performance. Properties of the approximation functions are outlined in detail. All convergence results of the traditional methods are preserved. 相似文献
996.
For a strictly decreasing sequence an
n=0 of nonnegative real numbers converging to zero, we construct a continuous 2-periodic function f such that RT
n(f) = an, n=0,1,2,..., where RT
n(f) are best approximations of the function f in uniform norm by trigonometric rational functions of degree at most n. 相似文献
997.
Monika Ludwig 《Mathematische Nachrichten》2001,227(1):99-108
Let Hj(K, ·) be the j – th elementary symmetric function of the principal curvatures of a convex body K in Euclidean d – space. We show that the functionals ∫bd f(Hj(K, x)) dℋ︁d—1(x) depend upper semicontinuously on K, if f : [0, ∞) is concave, limt→0f(t) = 0, and limt→∞f(t)/t = 0. An analogous statement holds for integrals of elementary symmetric functions of the principal radii of curvature. 相似文献
998.
A. Melman. 《Mathematics of Computation》2001,70(234):649-669
We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.
999.
一类奇异二阶系统边值问题的正解 总被引:6,自引:0,他引:6
本文利用正规锥和迭代法考察了一类奇异二阶系统边值问题的正解的存在性.我们的工作是对[1]的补充和发展. 相似文献
1000.
Banach空间的p— Asplund 伴随空间 总被引:3,自引:1,他引:3
程立新 《应用泛函分析学报》2001,3(2):120-128
我们称一个定义在Banach空间E上的连续凸函数f具有Frechet可微性质(FDP),如果E上的每个实值凸函数g≤f均在E一个稠密的Gδ-子集上Frechet可微。本文主要证明了:对任何Banach空间E,均存在一个局部凸相容拓扑p使得1)(E,p)是Hausdorff局部凸空间;2) E上的每个范数连续具有FDP的凸函数均是p-连续的;3)每个p-连续的凸函数均具有FDP ;4)p等价某个范数拓扑当且仅不E是Asplund空间。 相似文献