25,653 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
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
Riemannian Conjugate Gradient Methods: General Framework and Specific Algorithms with Convergence Analyses
Conjugate gradient methods are important first-order optimization algorithms both in Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate gradient methods have been studied in Euclidean spaces, there are relatively fewer studies for those on Riemannian manifolds (i.e., Riemannian conjugate gradient methods). This paper proposes a novel general framework that unifies existing Riemannian conjugate gradient methods such as the ones that utilize a vector transport or inverse retraction. The proposed framework also develops other methods that have not been covered in previous studies. Furthermore, conditions for the convergence of a class of algorithms in the proposed framework are clarified. Moreover, the global convergence properties of several specific types of algorithms are extensively analyzed. The analysis provides the theoretical results for some algorithms in a more general setting than the existing studies and new developments for other algorithms. Numerical experiments are performed to confirm the validity of the theoretical results. The experimental results are used to compare the performances of several specific algorithms in the proposed framework
A New CG-Algorithm with Self-Scaling VM-Update for Unconstraint Optimization
In this paper, a new combined extended Conjugate-Gradient (CG) and Variable-Metric (VM) methods is proposed for solving unconstrained large-scale numerical optimization problems. The basic idea is to choose a combination of the current gradient and some pervious search directions as a new search direction updated by Al-Bayati\u27s SCVM-method to fit a new step-size parameter using Armijo Inexact Line Searches (ILS). This method is based on the ILS and its numerical properties are discussed using different non-linear test functions with various dimensions. The global convergence property of the new algorithm is investigated under few weak conditions. Numerical experiments show that the new algorithm seems to converge faster and is superior to some other similar methods in many situations
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
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