| In classic backpropagation nets, as introduced by Rumelhart et al. 1], the weights are modiied according to the method of steepest descent. The goal of this weight modiication is to minimise the error in net-outputs for a given training set. Basing upon Jacobs' work 2], we point out drawbacks of steepest descent and suggest improvements on it. These yield a backpropagation net, which adjusts ...

In this paper we use steepest descent method for solving zero-one nonlinear programming problem. Using penalty function we transform this problem to an unconstrained optimization problem and then by steepest descent method we obtain the original problem optimal solution. 2007 Elsevier Inc. All rights reserved.

Steepest descent is central in variational mathematics. We present a new transparent existence proof for curves of near-maximal slope — an influential notion of steepest descent in a nonsmooth setting. We moreover show that for semi-algebraic functions — prototypical nonpathological functions in nonsmooth optimization — such curves are precisely the solutions of subgradient dynamical systems.

The problem of output regulation of affine nonlinear systems with the relative degree not well defined by modified steepest descent control is studied. The modified steepest descent control is a dynamic feedback control which is generated by the trajectory following method. By assuming the system is minimum phase, output of the system can be regulated globally asymptotically.

A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by square Fredholm determinant a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives terms two-dimensional Riemann-Hilbert problem. We solve latter null limit making use Deift-Zhou steepest descent. reproduce exact octagonal anomalous dimension 't Hooft c...

x f(x, θ) log f(x, θ) exists for all θ and θ. In principle, one can apply the sum-product algorithm in order to find (1), which involves the following two steps [2]: 1. Determine f(θ) by sum-product message passing. 2. Maximization step: compute θmax △ = argmaxθ f(θ). This procedure is often not feasible, since • When the variable x is continuous, the sum-product rule may lead to intractable in...

In this paper, the methods for use of prior information about multiple operating environments, in improving adaptive filter convergence properties are discussed. More concretely, the gain selection, profiling and scheduling in steepest descent algorithms are treated in detail. Work presented in this paper is an extension of [1]. Two flavors of optimization are discussed: average descent rate op...