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91.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
92.
Regina S. Burachik Rafail N. Gasimov Nergiz A. Ismayilova C. Yalçin. Kaya 《Journal of Global Optimization》2006,34(1):55-78
We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented
Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal
and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the
step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and
an optimal control problem.
*Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2.
Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA. 相似文献
93.
We have used x-ray fluorescence analysis to study the elemental composition of gunshot residues from smooth-bore and rifled-bore
guns. We have established that it is possible to differentiate between types of projectiles (jacketed/lead), types of primers
(corrosive/noncorrosive), and types of propellant powders (black/smokeless) by analysis of the elemental composition of the
gunshot residues. We have shown that the mercury content in gunshot residues on the surface of the object carrying the residues
steadily decreases as storage time increases. Despite this fact, mercury can be preserved as a component of gunshot residues
on the object (cotton cloth) under room conditions for more than 45 days.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 3, pp. 320–325, May–June, 2006. 相似文献
94.
The refractive indices (n) of eight standard oils from Physikalisch Technische Bundesanstalt, Germany were determined with an accuracy of ±1×10−4 by using Abbe Refractometer. The measurements were performed at temperature 20°C in the spectral range 0.4–0.7 μm. The experimental data were fitted to the simple Cauchy dispersion formula and the results were found to be consistent within the limits of experimental error. In all cases, the refractive index decreased monotonically with increasing wavelength. The refractive indices (n) of these oils have been measured as a function of the temperature t (20°C up to 50°C) at λ=0.589 μm and were found to have linear temperature dependencies. The refractive indices of the studied oils and the uncertainty in their values are calculated at λ=0.589. The Lorentz–Lorenz (L–L) formula has been tested and it was found to be valid with a maximum deviation of 0.4% and was used to calculate the molecular polarizability θ. 相似文献
95.
合成了两种新型噻吩基卟啉-5,15-二(2-噻吩基)-2,8,12,18-四乙基-3,7,13,17-四甲基卟啉7a(45.1%)和5,15-二(2-联噻吩基)-2,8,12,18-四乙基-3,7,13,17-四甲基卟啉7b(61.2%),并研究了它们的光谱性质,其中荧光光谱的最大发射峰蜂都在631nm处,量子产率分别为4.1%(7a)和1.4%(7b)。 相似文献
96.
In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints. 相似文献
97.
对Sn-C60薄膜进行紫外可见光吸收,X-射线衍射和扫描电镜的测定结果显示,薄膜样品紫外可见光吸收的两个短波段吸收峰比纯C60薄膜的吸收峰显著下降,说明Sn-C60薄膜的电子光吸收跃迁为间接跃迁,能带中有杂质能级的存在;样品的X射线衍射峰则对应于面心立方结构;扫描电镜结果显示薄膜为纳米级颗粒组成。 相似文献
98.
This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The
method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction
uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with
desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous
perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application
case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency
and efficiency in finding global optimal solutions, and is particularly useful for expensive systems. 相似文献
99.
M. A. Posypkin I. Kh. Sigal 《Computational Mathematics and Mathematical Physics》2006,46(12):2187-2202
The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered. 相似文献
100.
Silvia Vogel 《Annals of Operations Research》2006,142(1):269-282
The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution
will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence
statements for suitable functions of random sets are proved and the results are employed to derive stability statements for
random optimization problems where the objective function and the constraint set are approximated simultaneously.
The author is grateful to two anonymous referees for helpful suggestions. 相似文献