31,729 research outputs found
A COMPARATIVE STUDY OF SOME MODIFICATIONS OF CG METHODS UNDER EXACT LINE SEARCH
Conjugate Gradient (CG) method is a technique used in solving nonlinear unconstrained optimization problems. In this paper, we analysed the performance of two modifications and compared the results with the classical conjugate gradient methods of. These proposed methods possesse global convergence properties for general functions using exact line search. Numerical experiments show that the two modifications are more efficient for the test problems compared to classical CG coefficients
Two Versions of the Spectral Nonlinear Conjugate Gradient Method
The nonlinear conjugate gradient method is widely used to solve unconstrained optimization problems. In this paper the development of different versions of nonlinear conjugate gradient methods with global convergence properties proved. Numerical results indicated that the proposed method is very efficient
Global convergence properties of conjugate gradient methods for optimization
Projet PROMATHWe study the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches. The analysis covers two classes of methods that are globally convergent on smooth, non convex functions. Some properties of the Fletcher-Reeves method play an important role in the first family, whereas the second family shares an important property with the Polak-Ribiere method. Numerical experiments are presented
A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization
Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we present a specific three-term conjugate gradient method based on the multi-step quasi-Newton method. Finally, some numerical results of the proposed method are given
On Algorithms Based on Joint Estimation of Currents and Contrast in Microwave Tomography
This paper deals with improvements to the contrast source inversion method
which is widely used in microwave tomography. First, the method is reviewed and
weaknesses of both the criterion form and the optimization strategy are
underlined. Then, two new algorithms are proposed. Both of them are based on
the same criterion, similar but more robust than the one used in contrast
source inversion. The first technique keeps the main characteristics of the
contrast source inversion optimization scheme but is based on a better
exploitation of the conjugate gradient algorithm. The second technique is based
on a preconditioned conjugate gradient algorithm and performs simultaneous
updates of sets of unknowns that are normally processed sequentially. Both
techniques are shown to be more efficient than original contrast source
inversion.Comment: 12 pages, 12 figures, 5 table
Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems
We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations.
We can compute branches of solutions with limit points, bifurcation points, etc.
Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations
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