In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test probl...

We study the effects of control domain position on optimal control problem of cardiac arrhythmia. The well-established mathematical model, namely, the monodomain model, is used to represent the electrical behavior of the cardiac tissue. Two test cases are considered in this paper: the control domain for Test Case 1 is close to the excitation domain, while the control domain for Test Case 2 is a...

In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large pen...

Aggregation-based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model twodimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysis ...

A two-dimensional shape identification problem, i.e. inverse geometry problem, of estimating simultaneously two interfacial configurations in a multiple (three) region domain is solved in this study by using the Conjugate Gradient Method (CGM) and Boundary Element Method (BEM)-based inverse algorithm. Two over-utilized conditions should be applied in determining two gradient equations, this dif...

The conjugate gradient method is an iterative technique used to solve systems of linear equations. The paper analyzes the performance of parallel preconditioned conjugate gradient algorithms. First, a theoretical model is proposed for estimation of the complexity of PPCG method and a scalability analysis is done for three different data decomposition cases. Computational experiments are done on...

This paper presents the hybrid algorithm of global optimization of dynamic learning rate for multilayer feedforward neural networks (MLFNN). The effect of inexact line search on conjugacy was studied and a generalized conjugate gradient method based on this effect was proposed and shown to have global convergence for error backpagation of MLFNN. The descent property and global convergence was g...

Discretizing the elliptic Poisson equation with homogeneous Dirichlet boundary conditions by the finite difference method results in a system of linear equations with a large, sparse, highly structured system matrix. It is a classical test problem for comparing the performance of direct and iterative linear solvers. We compare in this report Gaussian elimination applied to a dense system matrix...