Merlin-3.0 A multidimensional optimization environment

Papageorgiou, D.G.; Demetropoulos, Ioannis N.; Lagaris, Isaac E.

doi:10.1016/s0010-4655(98)00005-8

Cited by 40 publications

(35 citation statements)

References 24 publications

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“…Such packages provide a variety of optimization techniques that the user may employ to solve minimization problems. In our work we used the Merlin optimization package [21] that we had also employed previously for e ective training of multilayer perceptrons [20]. Another drawback of the quasi-Newton methods is that they cannot be used for on-line learning problems, since they operate in a`batch' mode.…”

Section: Resultsmentioning

confidence: 99%

“…We shall describe two popular formulas for updating B k , the BFGS update formula and the DFP update formula [5,21]. Let d p k 1 À p k and c g k 1 À g k .…”

Section: Training Using Quasi-newton Methodsmentioning

confidence: 99%

“…More speci®cal-ly, we use quasi-Newton optimization methods, which exploit gradient information to approximate the Hessian matrix of the error function with respect to the parameters of the network. This approximation matrix is subsequently used to determine an e ective search direction and update the values of the parameters in a manner analogous to Newton's method [5,16,21]. Quasi-Newton methods are generally considered more powerful compared to gradient-descent and their applications to the training of other neural network methods (multilayer perceptrons) was very successful [3,20].…”

Section: Introductionmentioning

confidence: 99%

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Training the random neural network using quasi-Newton methods

Likas

Stafylopatis

2000

European Journal of Operational Research

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Training in the random neural network (RNN) is generally speci®ed as the minimization of an appropriate error function with respect to the parameters of the network (weights corresponding to positive and negative connections). We propose here a technique for error minimization that is based on the use of quasi-Newton optimization techniques. Such techniques o er more sophisticated exploitation of the gradient information compared to simple gradient descent methods, but are computationally more expensive and di cult to implement. In this work we specify the necessary details for the application of quasi-Newton methods to the training of the RNN, and provide comparative experimental results from the use of these methods to some well-known test problems, which con®rm the superiority of the approach. Ó

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Section: Resultsmentioning

confidence: 99%

“…We shall describe two popular formulas for updating B k , the BFGS update formula and the DFP update formula [5,21]. Let d p k 1 À p k and c g k 1 À g k .…”

Section: Training Using Quasi-newton Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Training the random neural network using quasi-Newton methods

Likas

Stafylopatis

2000

European Journal of Operational Research

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“…In this way, the problem is transformed into the following constrained minimization problem: (5) subject to the constraints imposed by the BCs Dirichlet (6) or Neumann…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…More specifically, the proposed approach is based on the synergy of two feedforward ANNs of different types: a multilayer perceptron (MLP) as the basic approximation element and a radial basis function (RBF) network used to satisfy the boundary conditions (BCs). In addition, our approach relies on the availability of efficient multidimensional optimization software [5], that is used for the neural network training.…”

Section: Introductionmentioning

confidence: 99%

Neural-network methods for boundary value problems with irregular boundaries

Lagaris

Likas

Papageorgiou

2000

IEEE Trans. Neural Netw.

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461

243

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Abstract-Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the exact satisfaction of the boundary conditions. The method has been successfully tested on two-dimensional and three-dimensional PDEs and has yielded accurate results.Index Terms-Boundary value problems, engineering problems, irregular boundaries, neural networks, partial differential equations (PDEs), penalty method, multilayer perceptron, radial basis function (RBF) networks.

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Crack and Flaw Identification in Statics and Dynamics, using Filter Algorithms and Soft Computing

Stavroulakis

Engelhardt

Antes

Parameter Identification of Materials and Structures

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Merlin-3.0 A multidimensional optimization environment

Cited by 40 publications

References 24 publications

Training the random neural network using quasi-Newton methods

Training the random neural network using quasi-Newton methods

Neural-network methods for boundary value problems with irregular boundaries

Crack and Flaw Identification in Statics and Dynamics, using Filter Algorithms and Soft Computing

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