We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the periodic (and slightly more generally of the quasi-periodic finite-gap) Toda lattice for decaying initial data in the soliton region. In addition, we show how to reduce the problem in the remaining region to the known case without solitons.

This paper considers a method for dealing with non-convex objective functions in optimization problems. It uses the Hessian matrix and combines features of trust-region techniques and continuous steepest descent trajectory-following in order to construct an algorithm which performs curvilinear searches away from the starting point of each iteration. A prototype implementation yields promising r...

None of the existing methods for computing the oscillatory integral ∫ b a f(x)e iωg(x) dx achieve all of the following properties: high asymptotic order, stability, avoiding the computation of the path of steepest descent and insensitivity to oscillations in f . We present a new method that satisfies these properties, based on applying the gmres algorithm to a preconditioned differential operator.

In this paper, we investigate a steepest descent neural network for solving general nonsmooth convex optimization problems. The convergence to optimal solution set is analytically proved. We apply the method to some numerical tests which confirm the effectiveness of the theoretical results and the performance of the proposed neural network.

Two applications of a method of steepest descent (on the absolute magnitude of the system-equationsatisfaction error) are reported. In the first, simultaneous automatic analog determination of four coeffcients in a human response equation (transfer function) was accomp1ished. The second app1ication of the technique was in an analog dete~nat10n of aerodynamic coefficients from simulated flight t...

In this article, we present a geometric framework to study invariant sets of dynamical systems associated with differential equations. This framework is based on properties of invariant sets for an area functional. We obtain existence results for heteroclinic and periodic orbits. We also implement this approach numerically by means of the steepest descent method.

Abstract In this paper, we study a first-order solution method for particular class of set optimization problems where the concept is given by approach. We consider case in which set-valued objective mapping identified finite number continuously differentiable selections. The corresponding problem then equivalent to find optimistic solutions vector under uncertainty with set. develop optimality...

A steepest descent approximation scheme is derived for a recently developed model for the dynamics of the actin cytoskeleton in the lamellipodia of living cells. The scheme is used as a numerical method for the simulation of thought experiments, where a lamellipodial fragment is pushed by a pipette, and subsequently changes its shape and position.

We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularizationmethod. Numerical tests are presented for a linear problem related to photoacoustic tomography and a non-linear problem related to the testing of semiconductor ...

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable any line-search method. In particular, we combine Newton-type directions with scaled SD steps have suitable descent directions. Scaling step length makes significant difference respect similar approaches, terms b...