We present a new Hessian estimator based on the simultaneous perturbation procedure, that requires three system simulations regardless of the parameter dimension. We then present two newton-based simulation optimizati...
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We present a new Hessian estimator based on the simultaneous perturbation procedure, that requires three system simulations regardless of the parameter dimension. We then present two newton-based simulation optimization algorithms that incorporate this Hessian estimator. The two algorithms differ primarily in the manner in which the Hessian estimate is used. Both our algorithms do not compute the inverse Hessian explicitly, thereby saving on computational effort. While our first algorithm directly obtains the product of the inverse Hessian with the gradient of the objective, our second algorithm makes use of the Sherman-Morrison matrix inversion lemma to recursively estimate the inverse Hessian. We provide proofs of convergence for both our algorithms. Next, we consider an interesting application of our algorithms on a problem of road traffic control. Our algorithms are seen to exhibit better performance than two newton algorithms from a recent prior work.
The development and use of forward-looking macromodels in policy making institutions has proceeded at a much slower pace than what was predicted in the early 1980s. An important reason for this is that researchers hav...
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The development and use of forward-looking macromodels in policy making institutions has proceeded at a much slower pace than what was predicted in the early 1980s. An important reason for this is that researchers have not had access to robust and efficient solution techniques for solving nonlinear forward-looking models. This paper discusses the properties of alternative algorithms for solving MULTIMOD, the IMF's multicountry model of the world economy. Relative to traditional first-order algorithms in use today, we find that newton-based techniques are considerably faster and much less prone to simulation failure. (C) 1998 Elsevier Science B.V. All rights reserved.
In this article, various numerical methods to solve multicontact problems within the nonsmooth discrete element method are presented. The techniques considered to solve the frictional unilateral conditions are based b...
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In this article, various numerical methods to solve multicontact problems within the nonsmooth discrete element method are presented. The techniques considered to solve the frictional unilateral conditions are based both on the bipotential theory introduced by G. de Saxce and the augmented Lagrangian theory introduced by P. Alart. Following the ideas of Z.-Q. Feng a new newton method is developed to improve these classical algorithms, and numerical experiments are presented to show that these methods are faster than the previous ones, provide results with a better quality, and are less sensitive to the numerical parameters. Moreover, a stopping criterion that ensures a good mechanical property of the solution is provided. Copyright (c) 2012 John Wiley & Sons, Ltd.
Support vector machine (SVM) has always been one of the most successful learning methods, with the idea of structural risk minimization which minimizes the upper bound of the generalization error. Recently, a tighter ...
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Support vector machine (SVM) has always been one of the most successful learning methods, with the idea of structural risk minimization which minimizes the upper bound of the generalization error. Recently, a tighter upper bound of the generalization error, related to the variance of loss, is proved as the empirical Bernstein bound. Based on this result, we propose a novel risk-averse support vector classifier machine (RA-SVCM), which can achieve a better generalization performance by considering the second order statistical information of loss function. It minimizes the empirical first- and second-moments of loss function, i.e., the mean and variance of loss function, to achieve the "right" bias-variance trade-off for general classes. The proposed method can be solved by the kernel reduced and newton-type technique under certain conditions. Empirical studies show that the RA-SVCM achieves the best performance in comparison with other classical and state of art methods. The additional analysis shows that the proposed method is insensitive to the parameters, so abroad range of parameters lead to satisfactory performance. The proposed method is a general form of standard SVM, so it enriches the related studies of SVM.
Neural networks are receiving attention as controllers for many industrial applications. Although these networks eliminate the need for mathematical models, they require a lot of training to understand the model of a ...
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Neural networks are receiving attention as controllers for many industrial applications. Although these networks eliminate the need for mathematical models, they require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. This paper discusses the application of neural networks to control induction machines using direct torque control (DTC), A neural network is used to emulate the state selector of the DTC, The training algorithms used in this paper are the backpropagation, adaptive neuron model, extended Kalman filter, and the parallel recursive prediction error, Computer simulations of the motor and neural-network system using the four approaches are presented and compared, Discussions about the parallel recursive prediction error and the extended Kalman filter algorithms as the most promising training techniques is presented, giving their advantages and disadvantages.
Based on Hoeffding's inequality, many popular regression and classification models in supervised learning relax the expected risk minimization problem to the empirical risk minimization problem. Nevertheless, the ...
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Based on Hoeffding's inequality, many popular regression and classification models in supervised learning relax the expected risk minimization problem to the empirical risk minimization problem. Nevertheless, the recent theoretical results disclose that the bound of Bernstein's inequality -which includes variance information -is often significantly tighter than the bound of Hoeffding's inequality. In this paper, based on the empirical Bernstein bound, we proposed a risk-averse learning machine, which can achieve better generalization performance by trading off good loss performance (approximation error) and small vari-ance (estimation error) as well as suitable complexity of the model. We prove that the resulting learning machine is tractable for many popular loss functions. Moreover, to solve our model which is mostly non-convex because of the square root term, we introduce an extra variable to get rid of the square root and obtain an optimization problem that is convex in most cases for two variables respectively. Then newton's method can be used to solve it alternately. The experimental results on artificial and bench-mark datasets demonstrate that the proposed models can achieve better performance compared to other existing empirical risk minimization models.(c) 2023 Elsevier B.V. All rights reserved.
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