A general family of modified BFGS methods for unconstrained optimization
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In this paper, we present a general family of modified BFGS methods for unconstrained optimization. Under a general form of modified BFGS methods with an undetermined weight function, the family is constructed by determining the weight function based on the analysis of the approximation error to the Hessian matrix. This process gives rise to a novel family of modified BFGS methods with one free parameter, which includes several known methods as special cases. Both the global convergence and the local superlinear convergence rate of the new parametric family are proved under some mild conditions. We present how to choose the best values of the parameter to provide new methods with good performance. We conducted numerical experiments to compare the performance of the proposed methods with existing ones to choose the best method.
Abstract
In this paper, we present a general family of modified BFGS methods for unconstrained optimization. Under a general form of modified BFGS methods with an undetermined weight function, the family is constructed by determining the weight function based on the analysis of the approximation error to the Hessian matrix. This process gives rise to a novel family of modified BFGS methods with one free parameter, which includes several known methods as special cases. Both the global convergence and the local superlinear convergence rate of the new parametric family are proved under some mild conditions. We present how to choose the best values of the parameter to provide new methods with good performance. We conducted numerical experiments to compare the performance of the proposed methods with existing ones to choose the best method.