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111.
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113.
H. P. Benson 《Journal of Optimization Theory and Applications》2002,112(1):1-29
This article presents a branch-and-bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm economizes the required computations by conducting the branch-and-bound search in p, rather than in n, where p is the number of ratios in the objective function of problem (P) and n is the number of decision variables in problem (P). To implement the algorithm, the main computations involve solving a sequence of convex programming problems for which standard algorithms are available. 相似文献
114.
We prove some limiting results for a Lévy process X
t
as t0 or t, with a view to their ultimate application in boundary crossing problems for continuous time processes. In the present paper we are mostly concerned with ideas related to relative stability and attraction to the normal distribution on the one hand and divergence to large values of the Lévy process on the other. The aim is to find analytical conditions for these kinds of behaviour which are in terms of the characteristics of the process, rather than its distribution. Some surprising results occur, especially for the case t0; for example, we may have X
t
/t
P
+ (t0) (weak divergence to +), whereas X
t
/t a.s. (t0) is impossible (both are possible when t), and the former can occur when the negative Lévy spectral component dominates the positive, in a certain sense. Almost sure stability of X
t
, i.e., X
t
tending to a nonzero constant a.s. as t or as t0, after normalisation by a non-stochastic measurable function, reduces to the same type of convergence but with normalisation by t, thus is equivalent to strong law behaviour. Boundary crossing problems which are amenable to the methods we develop arise in areas such as sequential analysis and option pricing problems in finance. 相似文献
115.
Zoltán Megyesi 《Journal of Theoretical Probability》2002,15(4):973-1005
Max-semistable laws arise as non-degenerate weak limits of suitably centered and normed maxima of i.i.d. random variables along subsequences {k(n)} such that k(n+1)/k(n)c1, in which case the common distribution function F of the i.i.d. random variables is said to belong to the domain of geometric partial attraction of the max-semistable law. We give a necessary and sufficient condition for F to belong to the domain of geometric partial attraction of a max-semistable law and investigate the structure of these domains. We show that although weak convergence does not take place along {n}=, the distributions of the maxima merge together along the entire {n} with a suitably chosen family of limiting laws. The use of merge is demonstrated by almost sure limit theorems, which are also valid along the whole {n}. 相似文献
116.
Yuxiang Li Weibing Deng Chunhong Xie 《Proceedings of the American Mathematical Society》2002,130(12):3661-3670
The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
117.
有阻尼Sine-Gordon方程的全局吸引子的维数 总被引:4,自引:0,他引:4
本文通过引入新范数,得到有阻尼Sine-Gordon方程的Dirichlet问题的全局吸引子的维数的一个估计.结果表明:当“阻尼”与“扩散”同时增大或正弦项系数减小时,吸引子的维数减小.特别地,得到了零维吸引子存在的参数条件. 相似文献
118.
Lipschitzian optimization without the Lipschitz constant 总被引:30,自引:0,他引:30
D. R. Jones C. D. Perttunen B. E. Stuckman 《Journal of Optimization Theory and Applications》1993,79(1):157-181
We present a new algorithm for finding the global minimum of a multivariate function subject to simple bounds. The algorithm is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. This is done by carrying out simultaneous searches using all possible constants from zero to infinity. On nine standard test functions, the new algorithm converges in fewer function evaluations than most competing methods.The motivation for the new algorithm stems from a different way of looking at the Lipschitz constant. In particular, the Lipschitz constant is viewed as a weighting parameter that indicates how much emphasis to place on global versus local search. In standard Lipschitzian methods, this constant is usually large because it must equal or exceed the maximum rate of change of the objective function. As a result, these methods place a high emphasis on global search and exhibit slow convergence. In contrast, the new algorithm carries out simultaneous searches using all possible constants, and therefore operates at both the global and local level. Once the global part of the algorithm finds the basin of convergence of the optimum, the local part of the algorithm quickly and automatically exploits it. This accounts for the fast convergence of the new algorithm on the test functions. 相似文献
119.
120.
Giampaolo?Liuzzi Stefano?LucidiEmail author Veronica?Piccialli Antonello?Sotgiu 《Mathematical Programming》2004,101(2):339-364
In this paper we are concerned with the design of a small low-cost, low-field multipolar magnet for Magnetic Resonance Imaging with a high field uniformity. By introducing appropriate variables, the considered design problem is converted into a global optimization one. This latter problem is solved by means of a new derivative free global optimization method which is a distributed multi-start type algorithm controlled by means of a simulated annealing criterion. In particular, the proposed method employs, as local search engine, a derivative free procedure. Under reasonable assumptions, we prove that this local algorithm is attracted by global minimum points. Additionally, we show that the simulated annealing strategy is able to produce a suitable starting point in a finite number of steps with probability one.This work was supported by CNR/MIUR Research Program Metodi e sistemi di supporto alle decisioni, Rome, Italy.Mathematics Subject Classification (1991):65K05, 62K05, 90C56 相似文献