Displaying similar documents to “Conjugate gradient algorithm and fractals.”

A self-adaptive trust region method for the extended linear complementarity problems

Zhensheng Yu, Qiang Li (2009)

Applications of Mathematics

Similarity:

By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established...

A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

Zainab Hassan Ahmed, Mohamed Hbaib, Khalil K. Abbo (2024)

Applications of Mathematics

Similarity:

The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms...

Gradient descent and fast artificial time integration

Uri M. Ascher, Kees van den Doel, Hui Huang, Benar F. Svaiter (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

The integration to steady state of many initial value ODEs and PDEs using the forward Euler method can alternatively be considered as gradient descent for an associated minimization problem. Greedy algorithms such as steepest descent for determining the step size are as slow to reach steady state as is forward Euler integration with the best uniform step size. But other, much faster methods using bolder step size selection exist. Various alternatives are investigated from both theoretical...