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- W2743448588 abstract "Logarithmic Barrier Methods are studied and analyzed. Barrier methods form a class of Interior Point Methods that are used to solve general nonlinear constraint optimization problems. Usually, those methods move in a Newton-type direction. Emphasis is given on developing barrier methods for training supervised neural networks. Two algorithms are presented in this dissertation: a deterministic logarithmic barrier and a stochastic logarithmic barrier. Specifically, we consider neural network training as a nonlinear programming problem and use barrier methods to find the optimal weights. Furthermore, we put constraints on the weights to avoid network paralysis. The search direction is derived using a recursive prediction error method (RPEM) that approximates the inverse of the Hessian of a logarithmic error function iteratively. The weights move on a center trajectory in the interior of the feasible weight space and have good convergence properties. For the stochastic version, random fluctuations are added to the weights in order to escape local minima. Ill-conditioning problems are discussed and computational experiments are provided. Also, the deterministic logarithmic barrier is extended for the case where the error criterion is the least absolute error." @default.
- W2743448588 created "2017-08-17" @default.
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- W2743448588 date "1995-01-01" @default.
- W2743448588 modified "2023-09-27" @default.
- W2743448588 title "Logarithmic barrier functions and newton-type methods with applications to neural network training" @default.
- W2743448588 hasPublicationYear "1995" @default.
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