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Global convergence of a modified conjugate gradient method

Can Li, Ling Fang, Peng Lu

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Abstract

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. A modified conjugate gradient method is proposed in this paper for unconstrained optimization problems. The direction of the proposed method provides a descent direction for the objective function. Under mild conditions, we prove that the method with strong Wolfe line search is globally convergent.

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What this paper is about

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. A modified conjugate gradient method is proposed in this paper for unconstrained optimization problems. The direction of the proposed method provides a descent direction for the objective function. Under mild conditions, we prove that the method with strong Wolfe line search is globally convergent.

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Available abstract

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. A modified conjugate gradient method is proposed in this paper for unconstrained optimization problems. The direction of the proposed method provides a descent direction for the objective function. Under mild conditions, we prove that the method with strong Wolfe line search is globally convergent.

Key concepts: Conjugate gradient method, Nonlinear conjugate gradient method, Derivation of the conjugate gradient method, Gradient descent, Conjugate residual method, Convergence (economics), Gradient method, Descent (aeronautics)

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