3,521 research outputs found
Global convergence of new conjugate gradient method with inexact line search
In this paper, We propose a new nonlinear conjugate gradient method (FRA) that satisfies a sufficient descent condition and global convergence under the inexact line search of strong wolf powell. Our numerical experiment shaw the efficiency of the new method in solving a set of problems from the CUTEst package, the proposed new formula gives excellent numerical results at CPU time, number of iterations, number of gradient ratings when compared to WYL, DY, PRP, and FR methods
A Spectral Dai-Yuan-Type Conjugate Gradient Method for Unconstrained Optimization
A new spectral conjugate gradient method (SDYCG) is presented for solving unconstrained optimization problems in this paper. Our method provides a new expression of spectral parameter. This formula ensures that the sufficient descent condition holds. The search direction in the SDYCG can be viewed as a combination of the spectral gradient and the Dai-Yuan conjugate gradient. The global convergence of the SDYCG is also obtained. Numerical results show that the SDYCG may be capable of solving large-scale nonlinear unconstrained optimization problems
A dai-liao hybrid hestenes-stiefel and fletcher-revees methods for unconstrained optimization
Some problems have no analytical solution or too difficult to solve by scientists, engineers, and mathematicians, so the development of numerical methods to obtain approximate solutions became necessary. Gradient methods are more efficient when the function to be minimized continuously in its first derivative. Therefore, this article presents a new hybrid Conjugate Gradient (CG) method to solve unconstrained optimization problems. The method requires the first-order derivatives but overcomes the steepest descent method’s shortcoming of slow convergence and needs not to save or compute the second-order derivatives needed by the Newton method. The CG update parameter is suggested from the Dai-Liao conjugacy condition as a convex combination of Hestenes-Stiefel and Fletcher-Revees algorithms by employing an optimal modulating choice parameterto avoid matrix storage. Numerical computation adopts an inexact line search to obtain the step-size that generates a decent property, showing that the algorithm is robust and efficient. The scheme converges globally under Wolfe line search, and it’s like is suitable in compressive sensing problems and M-tensor systems
Improved Fletcher-Reeves Methods Based on New Scaling Techniques
This paper introduces a scaling parameter to the Fletcher-Reeves (FR) nonlinear conjugate gradient method. The main aim is to improve its theoretical and numerical properties when applied with inexact line searches to unconstrained optimization problems. We show that the sufficient descent and global convergence properties of Al-Baali for the FR method with a fairly accurate line search are maintained. We also consider the possibility of extending this result to less accurate line search for appropriate values of the scaling parameter. The reported numerical results show that several values for the proposed scaling parameter improve the performance of the FR method significantly
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
Modified memoryless spectral-scaling Broyden family on Riemannian manifolds
This paper presents modified memoryless quasi-Newton methods based on the
spectral-scaling Broyden family on Riemannian manifolds. The method involves
adding one parameter to the search direction of the memoryless self-scaling
Broyden family on the manifold. Moreover, it uses a general map instead of
vector transport. This idea has already been proposed within a general
framework of Riemannian conjugate gradient methods where one can use vector
transport, scaled vector transport, or an inverse retraction. We show that the
search direction satisfies the sufficient descent condition under some
assumptions on the parameters. In addition, we show global convergence of the
proposed method under the Wolfe conditions. We numerically compare it with
existing methods, including Riemannian conjugate gradient methods and the
memoryless spectral-scaling Broyden family. The numerical results indicate that
the proposed method with the BFGS formula is suitable for solving an
off-diagonal cost function minimization problem on an oblique manifold.Comment: 20 pages, 8 figure
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