A Practical Bundle Algorithm for Nonconvex and Nonsmooth Engineering Optimization and its Numerical Implementation

2000 ◽  
Author(s):  
Hong Wang-Zhou ◽  
Yifang Zhong ◽  
Renbin Xiao ◽  
Xuan Du ◽  
Ji Zhou
Keyword(s):  
Numerical Methods ◽  
Convergence Result ◽  
Numerical Results ◽  
Bundle Methods ◽  
Bundle Method ◽  
Engineering Optimization ◽  
Numerical Implementation ◽  
Practical Engineering ◽  
Bundle Algorithm

Abstract An algorithm based on Lemarechal’s bundle method for nonsmooth and nonconvex engineering optimization is proposed. The convergence result is given and proved. The algorithm’s numerical implementation is discussed in detail. By the numerical methods proposed by this paper, most bundle methods could be used in practical engineering optimization. Finally, some numerical results are presented to show its efficiency.

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Observations Regarding Numerical Results Obtained by the Floquet-Method

2013 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Monodromy Matrix ◽  
Mathieu Equation ◽  
Numerical Results ◽  
The Other ◽  
Benchmark Problem ◽  
Stability Studies ◽  
Floquet Method ◽  
System Equations ◽  
Time Periodic

Stability studies of parametrically excited systems are frequently carried out by numerical methods. Especially for LTP-systems, several such methods are known and in practical use. This study investigates and compares two methods that are both based on Floquet’s theorem. As an introductary benchmark problem a 1-dof system is employed, which is basically a mechanical representation of the damped Mathieu-equation. The second problem to be studied in this contribution is a time-periodic 2-dof vibrational system. The system equations are transformed into a modal representation to facilitate the application and interpretation of the results obtained by different methods. Both numerical methods are similar in the sense that a monodromy matrix for the LTP-system is calculated numerically. However, one method uses the period of the parametric excitation as the interval for establishing that matrix. The other method is based on the period of the solution, which is not known exactly. Numerical results are computed by both methods and compared in order to work out how they can be applied efficiently.

scholarly journals A PRACTICAL PERFORMANCE INDEX FOR COMPARING OF OPTIMIZATION SOFTWARE

2014 ◽  
pp. 7-12
Author(s):  
Andrea Attanasio ◽  
Patrizia Beraldi ◽  
Francesca Guerriero
Keyword(s):  
Numerical Methods ◽  
Performance Index ◽  
Relative Efficiency ◽  
Numerical Results ◽  
Optimization Software ◽  
Practical Performance

In this paper we propose a new practical performance index for ranking of numerical methods. This index may be very helpful especially when several methods are tested on a large number of instances, since it provides a concise and precise idea of the relative efficiency of a method with the respect to the others. In order to evaluate the efficiency of the proposed rule, we have applied it to the numerical results presented on previously published papers.

scholarly journals Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

2018 ◽  
Vol 7 (3.28) ◽  
pp. 89 ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Mustafa Mamat ◽  
Nurnadiah Zamri ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Computational Cost ◽  
Numerical Results ◽  
Parametric Form ◽  
Solution Point ◽  
New Ideas

New ideas on numerical methods for solving fuzzy nonlinear equations have spread quickly across the globe. However, most of the methods available are based on Newton’s approach whose performance is impaired by either discontinuity or singularity of the Jacobian at the solution point. Also, the study of dual fuzzy nonlinear equations is yet to be explored by many researchers. Thus, in this paper, a numerical method to investigate the solution of dual fuzzy nonlinear equations is proposed. This method reduces the computational cost of Jacobian evaluation at every iteration. The fuzzy coefficients are presented in its parametric form. Numerical results obtained have shown that the proposed method is efficient. 

Antialiasing condition and filter for the reciprocity equation of correlation type

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB219-WB224 ◽  
Author(s):  
Weiping Cao ◽  
Gerard T. Schuster
Keyword(s):  
Seismic Data ◽  
Seismic Profile ◽  
Numerical Results ◽  
Numerical Implementation ◽  
Vertical Seismic Profile ◽  
Vsp Data ◽  
And Migration

An antialiasing formula has been derived for interferometric redatuming of seismic data. More generally, this formula is valid for numerical implementation of the reciprocity equation of correlation type, which is used for redatuming, extrapolation, interpolation, and migration. The antialiasing condition can be, surprisingly, more tolerant of a coarser trace sampling compared to the standard antialiasing condition. Numerical results with synthetic vertical seismic profile (VSP) data show that interferometry artifacts are effectively reduced when the antialiasing condition is used as a constraint with interferometric redatuming.

NUCLEAR COLLISIONS MODELS WITH BOLTZMANN OPERATORS

2000 ◽  
Vol 10 (04) ◽  
pp. 479-505 ◽  
Author(s):  
S. DELLACHERIE ◽  
R. SENTIS
Keyword(s):  
Numerical Methods ◽  
Asymptotic Analysis ◽  
Numerical Results ◽  
Nuclear Collisions

We describe a model related to nuclear collisions using Boltzmann operators. An asymptotic analysis is performed concerning the gain operator for the outgoing particles. Some numerical methods related to this model are also described and numerical results are given.

An Interpolation-Based Method for Multidimensional Extrapolation

2014 ◽  
Vol 1079-1080 ◽  
pp. 654-659
Author(s):  
Ru Chao Shi ◽  
Yong Chi Li
Keyword(s):  
Numerical Results ◽  
Numerical Implementation ◽  
Order Accuracy ◽  
First Order ◽  
Numerical Tests ◽  
Pde Method ◽  
Theoretical Results

This paper presents an interpolation-based method for multidimensional extrapolation. A series of interpolation formulations are proposed to extrapolate functions normal to the interface between two regions. Theoretical proofs and relevant analysis are also presented. The method developed maintains the characteristics of implicit interface. The interface inside every cell is treated smoothly by assuming that curvature is equal everywhere. The method developed and numerical results are verified by comparing to the results by PDE method and theoretical results. Numerical tests demonstrate that the method developed is first-order accuracy and also more efficient in numerical implementation and more accurate than PDE method.

Mechanical Systems With Impacts: Comparison of Several Numerical Methods

1999 ◽  
Author(s):  
C. H. Lamarque ◽  
O. Janin
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Infinite Number ◽  
Mechanical Systems ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Periodic Behavior ◽  
Numerical Tests ◽  
Runge Kutta ◽  
Theoretical Results

Abstract We study the performances of several numerical methods (Paoli-Schatzman, Newmark, Runge-Kutta) in order to compute periodic behavior of a simple one-degree-of-freedom impacting oscillator. Some theoretical results are given and numerical tests are performed. We compare mathematical and numerical results using our simple example exhibiting either finite or infinite number of impacts per period. Comparison of exact and numerical solution provides a practical order for each scheme. We conclude about the use of the different numerical methods.

Determination of Parameter in SYS Cam-Clay Model of Ultra-Soft Clay

2015 ◽  
Vol 744-746 ◽  
pp. 470-473
Author(s):  
Bin Bin Xu ◽  
Toshihiro Noda
Keyword(s):  
Constitutive Model ◽  
Soil Structure ◽  
Soft Clay ◽  
Numerical Results ◽  
Plastic Model ◽  
Clay Model ◽  
The World ◽  
Practical Engineering ◽  
Cam Clay

Parameter analyses in the constitutive model determine the precision of numerical results. Cam-clay model is the first elasto-plastic model in the world and widely used in the practical engineering. SYS Cam-clay model is proposed based on Cam-clay model by incorporating the concept of overconsolidation, soil structure and anisotropy. There are two groups of parameters in this model, elasto-plastic parameters that are exactly same as those in Cam-clay model and evolutional parameters that decide the variation of overconsolidation, soil structure and anisotropy. The detailed process to determine the parameters is introduced step by step.

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