Because of their computing efficiency and minimal memory requirements, conjugate
gradient techniques are a fundamental family of algorithms for handling large-scale unconstrained
nonlinear optimization problems. A new version of the Hestenes-Stiefel (HS) technique is presented
in this study with the goal of improving convergence properties without compromising ease of use.
We rigorously prove the global convergence qualities of the proposed approach under standard
assumptions and show that it meets the conjugacy, descent, and adequate descent constraints.
Numerous numerical tests, covering a wide range of benchmark issues, show that the suggested
strategy routinely performs better than the traditional HS approach in terms of function evaluations
and iteration count.
2025-08
Science Journal of University of Zakho
(Issue : 2)
(Volume : 11)
THE NEW RANK ONE CLASS FOR UNCONSTRAINED PROBLEMS SOLVING
One of the most well-known methods is the quasi-Newton approach, iterative solutions for unconstrained problems. The great
precision and quick convergence of the quasi-Newton methods are well recognized. In this work, we derive the new algorithm for
the symmetric rank one SR1 method.
The strong Wolfe line search criteria define the step length selection. We also proved the new quasi-Newton equation and positive
definite matrix theorem. preliminary computer testing on the set of fourteen Unrestricted optimization test functions leads to the
conclusion that this new method is more effective and durable than the implementation of classical the SR1 method. In terms of
iterations count and functions.
2023-04
International Journal of Computer Mathematics
(Issue : 4)
(Volume : 100)
New spectral LS conjugate gradient method for nonlinear unconstrained optimization
In this work, we propose a novel algorithm to perform spectral conjugate
gradient descent for an unconstrained, nonlinear optimization problem.
First, we theoretically prove that the proposed method satisfies the sufficient
descent condition, the conjugacy condition, and the global convergence
theorem. The experimental setup uses Powell’s conjugacy condition
coupled with a cubic polynomial line search using strong Wolfe conditions
to ensure quick convergence. The experimental results demonstrate that
the proposed method shows superior performance in terms of the number
of iterations to convergence and the number of function evaluations when
compared to traditional methods such as Liu and Storey (LS) and Conjugate
Descent (CD).
2023-01
General Letters in Mathematics (GLM)
(Issue : 12)
(Volume : 1)
Conjugated Gradient with Four Terms for Nonlinear Unconstrained Optimization
The nonlinear conjugate gradient (GJG) technique is an effective tool for addressing minimization on a huge
scale. It can be used in a variety of applications., We presented a novel conjugate gradient approach based on two
hypotheses, and we equalized the two hypotheses and retrieved the good parameter in this article. To get a new
conjugated gradient, we multiplied the new parameter by a control parameter and substituted it in the second
equation. a fresh equation for 𝛽𝑘
is proposed. It has global convergence qualities. When compared to the two most
common conjugate gradient techniques, our algorithm outperforms them in terms of both the number of
iterations (NOIS) and the number of functions (NOFS). The new technique is efficient in real computing and
superior to previous comparable approaches in many instances, according to numerical results.
2022-05
Mathematics and Statistics
(Issue : 10)
(Volume : 2)
A New Algorithm for Spectral Conjugate Gradient in Nonlinear Optimization
CJG is a nonlinear conjugation gradient.
Algorithms have been used to solve large-scale
unconstrained enhancement problems. Because of their
minimal memory needs and global convergence qualities,
they are widely used in a variety of fields. This approach
has lately undergone many investigations and
modifications to enhance it. In our daily lives, the
conjugate gradient is incredibly significant. For example,
whatever we do, we strive for the best outcomes, such as
the highest profit, the lowest loss, the shortest road, or the
shortest time, which are referred to as the minimum and
maximum in mathematics, and one of these ways is the
process of spectral gradient descent. For multidimensional
unbounded objective function, the spectrum conjugated
gradient (SCJG) approach is a strong tool. In this study, we
describe a revolutionary SCG technique in which
performance is quantified. Based on assumptions, we
constructed the descent condition, sufficient descent
theorem, conjugacy condition, and global convergence
criteria using a robust Wolfe and Powell line search.
Numerical data and graphs were constructed utilizing
benchmark functions, which are often used in many
classical functions, to demonstrate the efficacy of the
recommended approach. According to numerical statistics,
the suggested strategy is more efficient than some current
techniques. In addition, we show how the unique method
may be utilized to improve solutions and outcomes.
2022-03
General Letters in Mathematics (GLM)
(Issue : 1)
(Volume : 11)
Global convergence of new three terms conjugate gradient for unconstrained optimization
Abstract
In this paper, a new formula of 𝛽𝑘
is suggested for the conjugate gradient method of solving unconstrained
optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent
condition, sufficient descent condition, conjugacy condition, and global convergence properties. Numerical
comparisons with two standard conjugate gradient algorithms show that this algorithm is very effective depending
on the number of iterations and the number of functions evaluated.
2021-10
Journal of University of Duhok (Pure and Eng. Sciences)
(Issue : 2)
(Volume : 24)
ENHANCE THE EFFICIENCY OF RMIL'S FORMULA FOR MINIMUM PROBLEM
In this paper, a new formula of 𝜷𝒌 is suggested for conjugate gradient method of solving unconstrained
optimization problems based on depends on the creation and update of RMIL’S formula with the inclusion of
a parameter and step size of cubic. Our novel proposed CG-method has descent condition and global
convergence properties. Numerical comparisons with standard conjugate gradient algorithm of RMIL’S
formula show that this algorithm very effective depending on the number of iterations and the number of
functions evaluation.
2021-10
International Journal of Advanced Research in Engineering & Management (IJAREM)
(Issue : 2)
(Volume : 1)
A New Conjugate Gradient for Nonlinear Unconstrained Optimization
The conjugate gradient method is a very useful technique for solving minimization problems
and has wide applications in many fields. In this paper we propose a new conjugate gradient methods by)
for nonlinear unconstrained optimization. The given method satisfies descent condition under strong Wolfe
line search andglobal convergence property for uniformly functions.Numerical results based on the number
of iterations (NOI)and number of function (NOF), have shown that the new 𝛽𝑘
𝑁𝑒𝑤
performs better thanas
Hestenes-Steifel(HS)CG methods.
2015-05
International Journal of Advanced Research in Engineering & Management (IJAREM)
(Issue : 1)
(Volume : 1)
A Modification of Quasi-Newton (DFP) Method for Solving Unconstrained Optimization Problems
The Quasi-Newton method is a very useful technique for solving minimization problems and
has wide applications in many fields. In this paper we develop a new class of DFP method for unconstrained
optimization. The given method satisfies the Quasi-Newton condition and positive definite theorem under
strong Wolfe line search. Numerical results based on the number of iterations (NOI) and number of function
(NOF), have shown that the new method (New5) performs better than standard method of ( ) method.
2015-04
International Journal of Enhanced Research in Science Technology & Engineering,
(Issue : 4)
(Volume : 4)
Improve Performance of Fletcher-Reeves (FR) Method
Conjugate gradient (CG) methods are famous for solving nonlinear unconstrained optimization problems
because they required low computational memory. In this paper, we propose a new conjugate gradient (𝛃𝐤
𝐍𝐞𝐰𝟏
)
which possesses global convergence properties using exact line search and inexact line search. The given method
satisfies sufficient descent condition under strong Wolfe line search. Numerical results based on the number of
iterations (NOI) and number of function (NOF), have shown that the new 𝛃𝐤
𝐍𝐞𝐰𝟏 performs better than Flecher-
Reeves (FR) CG methods.
2015-04
Thesis
2015-12-01
A New Self-Scaling Preconditioned Conjugate Gradient and Family of New Scaled CG for Nonlinear Unconstrained Optimization
