• 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 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.73-81
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• 2013

In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.239-254
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• 2006

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.