• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1303-1309
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• 2011

Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.129-142
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• 1998

In this paper, we propose a blocked variant of the Conjugate Gradient method which performs as well as and has coarser parallelism than the classical Conjugate Gradient method.

• Journal of the military operations research society of Korea
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• v.24 no.1
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.740-749
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• 1998

This paper proposes compression of image data using neural networks based on conjugate gradient method and dynamic tunneling system. The conjugate gradient method is applied for high speed optimization .The dynamic tunneling algorithms, which is the deterministic method with tunneling phenomenon, is applied for global optimization. Converging to the local minima by using the conjugate gradient method, the new initial point for escaping the local minima is estimated by dynamic tunneling system. The proposed method has been applied the image data compression of 12 ${\times}$12 pixels. The simulation results shows the proposed networks has better learning performance , in comparison with that using the conventional BP as learning algorithm.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.157-165
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• 2016

In this paper, we develop a new hybridization conjugate gradient method for solving the unconstrained optimization problem. Under mild assumptions, we get the sufficient descent property of the given method. The global convergence of the given method is also presented under the Wolfe-type line search and the general Wolfe line search. The numerical results show that the method is also efficient.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.353-363
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• 2013

A variant of the global conjugate gradient method for solving general linear systems with multiple right-hand sides is proposed. This method is called as the global conjugate gradient linear least squares (Gl-CGLS) method since it is based on the conjugate gradient least squares method(CGLS). We present how this method can be implemented for the image deblurring problems with Neumann boundary conditions. Numerical experiments are tested on some blurred images for the purpose of comparing the computational efficiencies of Gl-CGLS with CGLS and Gl-LSQR. The results show that Gl-CGLS method is numerically more efficient than others for the ill-posed problems.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.61-66
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• 2006

Two iterative solvers are applied to solve the modified mild slope equation. The elliptic formulation of the governing equation is selected for numerical treatment because it is partly suited for complex wave fields, like those encountered inside harbors. The requirement that the computational model should be capable of dealing with a large problem domain is addressed by implementing and testing two iterative solvers, which are based on the Stabilized Bi-Conjugate Gradient Method (BiCGSTAB) and Generalized Conjugate Gradient Method (GCGM). The characteristics of the solvers are compared, using the results for Berkhoff's shoal test, used widely as a benchmark in coastal modeling. It is shown that the GCGM algorithm has a better convergence rate than BiCGSTAB, and preconditioning of these algorithms gives more than half a reduction of computational cost.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1715-1725
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• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• Proceedings of the KOR-KST Conference
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• 1999.10a
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• pp.65-70
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• 1999