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A Modified BFGS Trust Region Method

Yunlong Lu, Xiaowei Jiang, Yueting Yang

Open publisher page 3 citations

Abstract

We propose a new trust region method that employs both the modified BFGS update and Amijio line search. The method exploits the information of function and gradient, and ensures the Hessian matrix of trust region subproblem positive-definite. At some assumptions, the global convergence and superlinear convergence property are proposed. Finally, numerical experiments show that the method is efficient.

About this research paper

What this paper is about

We propose a new trust region method that employs both the modified BFGS update and Amijio line search. The method exploits the information of function and gradient, and ensures the Hessian matrix of trust region subproblem positive-definite. At some assumptions, the global convergence and superlinear convergence property are proposed. Finally, numerical experiments show that the method is efficient.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

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Method / approach

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Available abstract

We propose a new trust region method that employs both the modified BFGS update and Amijio line search. The method exploits the information of function and gradient, and ensures the Hessian matrix of trust region subproblem positive-definite. At some assumptions, the global convergence and superlinear convergence property are proposed. Finally, numerical experiments show that the method is efficient.

Key concepts: Broyden–Fletcher–Goldfarb–Shanno algorithm, Hessian matrix, Trust region, Convergence (economics), Quasi-Newton method, Line search, Property (philosophy), Computer science

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