Limited memory technique using trust regions for nonlinear equations

作者：Huang, Linghua^*

来源：Applied Mathematical Modelling, 2015, 39(19): 5969-5981.

DOI：10.1016/j.apm.2015.06.003

• Limited memory BEGS method
• Trust region method
• Nonlinear equations
• Line search
• Global convergence

A new trust region subproblem that accelerates convergence for solving symmetric nonlinear equations is defined. To avoid repeatedly computing the trust region subproblem, a line search technique without derivative information is used in the trust region algorithm. Moreover, a limited memory BFGS update is employed to generate an approximated matrix rather than a normal Jacobian matrix or quasi-Newton matrix. Under mild conditions, the global convergence and the superlinear convergence of the given algorithm are established. The numerical results indicate that this method can be beneficial for solving the presented problems.

• 出版日期2015-10-1
• 单位广西财经学院