This paper is a continuation of [Rav02] and the second in a series of papers intended to clarify and expand results of the last chapter of [Rav04], in which we described a method for computing the Adams-Novikov E2-term and used it to determine the stable homotopy groups of spheres through dimension 108 for p = 3 and 999 for p = 5. The latter computation was a substantial improvement over prior ...

In this paper, we propose to train the RBF neural network using a global descent method. Essentially, the method imposes a monotonic transformation on the training objective to improve numerical sensitivity without altering the relative orders of all local extrema. A gradient descent search which inherits the global descent property is derived to locate the global solution of an error objective...

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover, the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm, espe...

For many years energy optimization has dealt with large scale mixed integer linear programs. The paper concentrates on programs that are used for controlling an existing generation system consisting of thermal power units and pumped hydro storage plants, therefore they should be solved in real time. The problem can be decomposed into smaller problems using Lagrangian Relaxation. One of these pr...

We consider the special case of the restarted Arnoldi method for approximating the product of a function of a Hermitian matrix with a vector which results when the restart length is set to one. When applied to the solution of a linear system of equations, this approach coincides with the method of steepest descent. We show that the method is equivalent with an interpolation process in which the...

We design and study an adaptive algorithm for the numerical solution of the stationary nonlinear Stokes problem. The algorithm can be interpreted as a disturbed steepest descent method, which generalizes Uzawa’s method to the nonlinear case. The outer iteration for the pressure is a descent method with fixed step-size. The inner iteration for the velocity consists of an approximate solution of ...

This paper reports preliminary results of our effort to address the acoustic-to-articulatory inversion problem. We tested an approach that simulates speech production acquisition as a distal learning task, with acoustic signals of natural utterances in the form of MFCC as input, VocalTractLab — a 3D articulatory synthesizer controlled by target approximation models as the learner, and stochasti...

in this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique....

27 information is used. A choice then has to be made as to which is the most eecient option. Acknowledgments. We are grateful to the referees for their useful comments. We thank Robert Michael Lewis for his valuable suggestions on how best to present this material, particularly the results given in x7. Mathematical models for the predictive value of early CA125 serum levels in epithelial ovaria...