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288
An introduction to the conjugate gradient method without the agonizing pain
, 1994
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GLOBAL CONVERGENCE PROPERTIES OF CONJUGATE GRADIENT METHODS FOR OPTIMIZATION
, 1992
"... This paper explores the convergence ofnonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes ofmethods that are globally convergent on smooth, nonconvex functions. Some properties of the FletcherReeves method play an important role ..."
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Cited by 102 (3 self)
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This paper explores the convergence ofnonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes ofmethods that are globally convergent on smooth, nonconvex functions. Some properties of the FletcherReeves method play an important role in the first family, whereas the second family shares an important property with the PolakRibire method. Numerical experiments are presented.
LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is ..."
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Cited by 100 (17 self)
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An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
Probabilistic Reasoning in Terminological Logics
, 1994
"... In this paper a probabilistic extensions for terminological knowledge representation languages is defined. Two kinds of probabilistic statements are introduced: statements about conditional probabilities between concepts and statements expressing uncertain knowledge about a specific object. The usua ..."
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Cited by 78 (5 self)
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In this paper a probabilistic extensions for terminological knowledge representation languages is defined. Two kinds of probabilistic statements are introduced: statements about conditional probabilities between concepts and statements expressing uncertain knowledge about a specific object. The usual modeltheoretic semantics for terminological logics are extended to define interpretations for the resulting probabilistic language. It is our main objective to find an adequate modelling of the way the two kinds of probabilistic knowledge are combined in commonsense inferences of probabilistic statements. Cross entropy minimization is a technique that turns out to be very well suited for achieving this end. 1 INTRODUCTION Terminological knowledge representation languages (concept languages, terminological logics) are used to describe hierarchies of concepts. While the expressive power of the various languages that have been defined (e.g. KLONE [BS85] ALC [SSS91]) varies greatly in that ...
The NEWUOA software for unconstrained optimization with derivatives
, 2004
"... Abstract: The NEWUOA software seeks the least value of a function F(x), x∈R n, when F(x) can be calculated for any vector of variables x. The algorithm is iterative, a quadratic model Q ≈ F being required at the beginning of each iteration, which is used in a trust region procedure for adjusting the ..."
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Cited by 76 (3 self)
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Abstract: The NEWUOA software seeks the least value of a function F(x), x∈R n, when F(x) can be calculated for any vector of variables x. The algorithm is iterative, a quadratic model Q ≈ F being required at the beginning of each iteration, which is used in a trust region procedure for adjusting the variables. When Q is revised, the new Q interpolates F at m points, the value m=2n+1 being recommended. The remaining freedom in the new Q is taken up by minimizing the Frobenius norm of the change to ∇ 2 Q. Only one interpolation point is altered on each iteration. Thus, except for occasional origin shifts, the amount of work per iteration is only of order (m+n) 2, which allows n to be quite large. Many questions were addressed during the development of NEWUOA, for the achievement of good accuracy and robustness. They include the choice of the initial quadratic model, the need to maintain enough linear independence in the interpolation conditions in the presence of computer rounding errors, and the stability of the updating of certain matrices that allow the fast revision of Q. Details are given of the techniques that answer all the questions that occurred. The software was tried on several test problems. Numerical results for nine of them are reported and discussed, in order to demonstrate the performance of the software for up to 160 variables.
A new conjugate gradient method with guaranteed descent and an efficient line search
 SIAM J. OPTIM
, 2005
"... A new nonlinear conjugate gradient method and an associated implementation, based on an inexact line search, are proposed and analyzed. With exact line search, our method reduces to a nonlinear version of the Hestenes–Stiefel conjugate gradient scheme. For any (inexact) line search, our scheme sat ..."
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Cited by 59 (6 self)
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A new nonlinear conjugate gradient method and an associated implementation, based on an inexact line search, are proposed and analyzed. With exact line search, our method reduces to a nonlinear version of the Hestenes–Stiefel conjugate gradient scheme. For any (inexact) line search, our scheme satisfies the descent condition gT k dk ≤ − 7 8 ‖gk‖2. Moreover, a global convergence result is established when the line search fulfills the Wolfe conditions. A new line search scheme is developed that is efficient and highly accurate. Efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer. High accuracy is achieved by using a convergence criterion, which we call the “approximate Wolfe ” conditions, obtained by replacing the sufficient decrease criterion in the Wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion. Numerical comparisons are given with both LBFGS and conjugate gradient methods using the unconstrained optimization problems in the CUTE library.
Comparative study of stock trend prediction using time delay, recurrent and probabilistic neural networks
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 1998
"... Three networks are compared for low false alarm stock trend predictions. Shortterm trends, particularly attractive for neural network analysis, can be used profitably in scenarios such as option trading, but only with significant risk. Therefore, we focus on limiting false alarms, which improves ..."
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Cited by 50 (0 self)
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Three networks are compared for low false alarm stock trend predictions. Shortterm trends, particularly attractive for neural network analysis, can be used profitably in scenarios such as option trading, but only with significant risk. Therefore, we focus on limiting false alarms, which improves the risk/reward ratio by preventing losses. To predict stock trends, we exploit time delay, recurrent, and probabilistic neural networks (TDNN, RNN, and PNN, respectively), utilizing conjugate gradient and multistream extended Kalman filter training for TDNN and RNN. We also discuss different predictability analysis techniques and perform an analysis of predictability based on a history of daily closing price. Our results indicate that all the networks are feasible, the primary preference being one of convenience.
A survey of nonlinear conjugate gradient methods. Available online at http://www.math.ufl.edu/~hager/papers/CG/cg_survey.pdf
, 2005
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A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
 SIAM J. Optim
, 1999
"... . Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. However, the strong Wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods. This paper presents a new version of the conjugate gradient method, w ..."
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Cited by 44 (7 self)
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. Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. However, the strong Wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods. This paper presents a new version of the conjugate gradient method, which converges globally provided the line search satisfies the standard Wolfe conditions. The conditions on the objective function are also weak, which are similar to that required by the Zoutendijk condition. Key words. unconstrained optimization, new conjugate gradient method, Wolfe conditions, global convergence. AMS subject classifications. 65k, 90c 1. Introduction. Our problem is to minimize a function of n variables min f(x); (1.1) where f is smooth and its gradient g(x) is available. Conjugate gradient methods for solving (1.1) are iterative methods of the form x k+1 = x k + ff k d k ; (1.2) where ff k ? 0 is a steplength, d k is a search direction. Normally the search direction at...
Comparison of support vector machine and artificial neural network systems for drug/ nNondrug classification
 J. Chem. Inf. Comput. Sci. 2003
"... Support vector machine (SVM) and artificial neural network (ANN) systems were applied to a drug/nondrug classification problem as an example of binary decision problems in earlyphase virtual compound filtering and screening. The results indicate that solutions obtained by SVM training seem to be mo ..."
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Cited by 42 (2 self)
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Support vector machine (SVM) and artificial neural network (ANN) systems were applied to a drug/nondrug classification problem as an example of binary decision problems in earlyphase virtual compound filtering and screening. The results indicate that solutions obtained by SVM training seem to be more robust with a smaller standard error compared to ANN training. Generally, the SVM classifier yielded slightly higher prediction accuracy than ANN, irrespective of the type of descriptors used for molecule encoding, the size of the training data sets, and the algorithm employed for neural network training. The performance was compared using various different descriptor sets and descriptor combinations based on the 120 standard GhoseCrippen fragment descriptors, a wide range of 180 different properties and physicochemical descriptors from the Molecular Operating Environment (MOE) package, and 225 topological pharmacophore (CATS) descriptors. For the complete set of 525 descriptors crossvalidated classification by SVM yielded 82% correct predictions (Matthews cc) 0.63), whereas ANN reached 80 % correct predictions (Matthews cc) 0.58). Although SVM outperformed the ANN classifiers with regard to overall prediction accuracy, both methods were shown to complement each other, as the sets of true positives, false positives (overprediction), true negatives, and false negatives (underprediction) produced by the two classifiers were not identical. The theory of SVM and ANN training is briefly reviewed.