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When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986. 相似文献
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基于BDF的无约束优化方法的收敛性分析 总被引:3,自引:0,他引:3
1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题 相似文献
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On the Application of the Auxiliary Problem Principle 总被引:6,自引:0,他引:6
The auxiliary problem principle (APP) derives from a general theory on decomposition-coordination methods establishing a comprehensive framework for both one-level and two-level methods. In this paper, the results of the two-level methods of APP are specialized for an efficient application to some engineering problems. 相似文献
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M. Ohsaki 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,73(3-4):241-251
Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point. 相似文献
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An Application of Branch and Cut to Open Pit Mine Scheduling 总被引:5,自引:0,他引:5
The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed. 相似文献
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This paper presents an analysis of a portfolio model which can be used to assist a property-liability insurance company in determining the optimal composition of the insurance and investment portfolios. By introducing insurer's threshold risk and relaxing some non-realistic assumptions made in traditional chance constraint insurance and investment portfolio models, we propose a method for an insurer to maximize his return threshold for a given threshold risk level. This proposed model can be used to optimize the composition of underwriting and investment portfolios regarding the insurer's threshold risk level, as well as to generate the efficient frontier by adjusting insurer's threshold risk levels. A numerical example is given based on the industry's aggregated data for a sixteen year period. 相似文献
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Dextran-modified iron oxide nanoparticles 总被引:1,自引:0,他引:1
Dextran-modified iron oxide nanoparticles were prepared by precipitation of Fe(Ⅱ) and Fe(Ⅲ) salts with ammonium hydroxide by two methods. Iron oxide was precipitated either in the presence of dextran solution, or the dextran solution was added after precipitation. In the second method, the iron oxide particle size and size distribution could be controlled depending on the concentration of dextran in the solution. The nanoparticles were characterized by size-exclusion chromatography, transmission electron microscopy and dynamic light scattering. Optimal conditions for preparation of stable iron oxide colloid particles were determined, The dextran/iron oxide ratio 0-0,16 used in precipitation of iron salts can be recommended for synthesis of nanoparticles suitable for biomedical applications, as the colloid does not contain excess dextran and does not coagulate. 相似文献
10.
Yu You George W. Kattawar Ping Yang Yong X. Hu Bryan A. Baum 《Journal of Quantitative Spectroscopy & Radiative Transfer》2006,100(1-3):470-482
Measurements from depolarized lidars provide a promising method to retrieve both cloud and aerosol properties and a versatile complement to passive satellite-based sensors. For lidar observations of clouds and aerosols, multiple scattering plays an important role in the scattering process. Monte Carlo simulations are carried out to investigate the sensitivity of lidar backscattering depolarization to cloud and aerosol properties. Lidar parameters are chosen to be similar to those of the upcoming space-based CALIPSO lidar. Cases are considered that consist of a single cloud or aerosol layer, as well as a case in which cirrus clouds overlay different types of aerosols. It is demonstrated that besides thermodynamic cloud phase, the depolarized lidar signal may provide additional information on ice or aerosol particle shapes. However, our results show little sensitivity to ice or aerosol particle sizes. Additionally, for the case of multiple but overlapping layers involving both clouds and aerosols, the depolarized lidar contains information that can help identify the particle properties of each layer. 相似文献