ADJOINT BROYDEN METHODS FOR SYMMETRIC NONLINEAR EQUATIONS

作者：Cao, Hui-Ping; Li, Dong-Hui^*

来源：Pacific Journal of Optimization, 2017, 13(4): 645-663.

• symmetric adjoint Broyden update
• nonlinear equations
• global convergence
• superlinear convergence
• automatic differentiation

In this paper, we adopt a technique similar to the derivation of Powell's Symmetric Broyden (PSB) method to obtain a new class of quasi-Newton methods which we call symmetric adjoint Broyden methods. The symmetric adjoint method shares some nice properties as its non-symmetric version. By the use of a nonmonotone line search, we show that the symmetric adjoint Broyden method with adjoint Broyden tangent update is globally and superlinearly convergent when applied to solve symmetric nonlinear equations. We also do some preliminary numerical experiments to test the performance of the proposed method. The numerical results indicate that the proposed method is effective and competitive.

• 出版日期2017-10