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2004•Journal of Huaihai Institute of TechnologyRequires access

A Class of Modified BFGS Algorithm Based on the New Quasi-Newton Equation

Haibin Wang

Open publisher page 3 citations

Abstract

A class of modified BFGS algorithm based on the new quasi-Newton equation Bk+1sk=k=yk+γksTksksk is presented in this paper to solve the unconstrained optimization problem, and the global convergence is proved under the condition that the objective function is uniformly convex, the parameter k satisfies |1-k|≤t′‖sk‖ (t′ is a constant). The update matrix generated by modified BFGS algorithm based on the new quasi-Newton equation is more approximate to Hessian matrix than the one based on the traditional quasi-Newton equation.

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What this paper is about

A class of modified BFGS algorithm based on the new quasi-Newton equation Bk+1sk=k=yk+γksTksksk is presented in this paper to solve the unconstrained optimization problem, and the global convergence is proved under the condition that the objective function is uniformly convex, the parameter k satisfies |1-k|≤t′‖sk‖ (t′ is a constant). The update matrix generated by modified BFGS algorithm based on the new quasi-Newton equation is more approximate to Hessian matrix than the one based on the traditional quasi-Newton equation.

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Available abstract

A class of modified BFGS algorithm based on the new quasi-Newton equation Bk+1sk=k=yk+γksTksksk is presented in this paper to solve the unconstrained optimization problem, and the global convergence is proved under the condition that the objective function is uniformly convex, the parameter k satisfies |1-k|≤t′‖sk‖ (t′ is a constant). The update matrix generated by modified BFGS algorithm based on the new quasi-Newton equation is more approximate to Hessian matrix than the one based on the traditional quasi-Newton equation.

Key concepts: Broyden–Fletcher–Goldfarb–Shanno algorithm, Hessian matrix, Quasi-Newton method, Mathematics, Constant (computer programming), Convergence (economics), Matrix (chemical analysis), Applied mathematics

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