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2014•Gongcheng shuxue xuebaoRequires access

A New Spectral Conjugate Gradient Method

Lin Sui-hu

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Abstract

Spectral conjugate gradient method contains two parameters for direction control,and it is a class of effective algorithms for unconstrained optimization problems. This paper presents a pair of formulas to create a new spectral conjugate gradient method, which is equivalent to the standard FR method when the line search is exact, and its intrinsic properties are similar to the standard DY method with Wolfe line search. The descent in each iteration and the global convergence of the new algorithm under Wolfe line search are proved. Preliminary numerical results show that the new algorithm is robust, effective and suitable for solving largescale unconstrained optimization problems.

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What this paper is about

Spectral conjugate gradient method contains two parameters for direction control,and it is a class of effective algorithms for unconstrained optimization problems. This paper presents a pair of formulas to create a new spectral conjugate gradient method, which is equivalent to the standard FR method when the line search is exact, and its intrinsic properties are similar to the standard DY method with Wolfe line search. The descent in each iteration and the global convergence of the new algorithm under Wolfe line search are proved. Preliminary numerical results show that the new algorithm is robust, effective and suitable for solving largescale unconstrained optimization problems.

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Available abstract

Spectral conjugate gradient method contains two parameters for direction control,and it is a class of effective algorithms for unconstrained optimization problems. This paper presents a pair of formulas to create a new spectral conjugate gradient method, which is equivalent to the standard FR method when the line search is exact, and its intrinsic properties are similar to the standard DY method with Wolfe line search. The descent in each iteration and the global convergence of the new algorithm under Wolfe line search are proved. Preliminary numerical results show that the new algorithm is robust, effective and suitable for solving largescale unconstrained optimization problems.

Key concepts: Conjugate gradient method, Nonlinear conjugate gradient method, Line search, Derivation of the conjugate gradient method, Conjugate residual method, Mathematics, Gradient descent, Gradient method

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