A modified BFGS algorithm based on a hybrid secant equation

作者：Babaie Kafaki Saman^*

来源：Science China Mathematics, 2011, 54(9): 2019-2036.

DOI：10.1007/s11425-011-4232-7

• unconstrained optimization
• hybrid secant equation
• BFGS update
• global convergence
• local and superlinear convergence

By making a convex combination of the modified secant equations proposed by Yuan and Wei et al., a hybrid secant equation and also, a modified BFGS algorithm is proposed. The hybridization parameter is effectively computed using the available information of recent iterations. Under proper conditions, it is shown that the proposed algorithm is globally, locally and superlinearly convergent. By using the performance profile introduced by Dolan and Mor,, a comparison between the implementations of the proposed algorithm and two efficient modified BFGS algorithms proposed by Yuan and Wei et al., on a set of unconstrained optimization test problems from the CUTEr collection, is done. Numerical results demonstrating the efficiency of the proposed modified BFGS algorithm are reported.

• 出版日期2011-9