A Linear Hybridization of the Hestenes-Stiefel Method and the Memoryless BFGS Technique

作者：Babaie Kafaki Saman^*; Ghanbari Reza

来源：Mediterranean Journal of Mathematics, 2018, 15(3): 86.

DOI：10.1007/s00009-018-1132-x

• Nonlinear programming
• unconstrained optimization
• conjugate gradient method
• memoryless BFGS method
• global convergence

We suggest a linear combination of search directions of the Hestenes-Stiefel method and the memoryless BFGS (Broyden-Fletcher-Goldfarb-Shanno) technique. As a result, a one-parameter extension of the Hestenes-Stiefel method is proposed. Based on an eigenvalue analysis, we show that the method may ensure the descent property. In a least-squares scheme, parameter of the method is determined in a way to tend the search direction of the method to the search direction of the three-term conjugate gradient method proposed by Zhang et al. which satisfies the sufficient descent condition. We conduct a brief global convergence analysis for the proposed method under the Wolfe line search conditions. Comparative numerical experiments are done on a set of the CUTEr test problems and the detailed results are reported. They show practical efficiency of the proposed method.

• 出版日期2018-6