A New Sparse Quasi-Newton UpdateMethod

Sultan Qaboos University Journal for Science

Rui Diao¹  Minghou Cheng¹  Yu-Hong Dai¹ 

[1] Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;

关键词: Large-scale, Matrix completion, Quasi-Newton methods, Secant condition, Sparsity, Unconstrained optimization.;   

DOI  :  10.24200/squjs.vol17iss1pp30-43

来源: DOAJ

【 摘 要 】

Based on the idea of maximum determinant positive definite matrix completion, Yamashita proposed a sparse quasi-Newton update, called MCQN, for unconstrained optimization problems with sparse Hessian structures. Such an MCQN update keeps the sparsity structure of the Hessian while relaxing the secant condition. In this paper, we propose an alternative to the MCQN update, in which the quasi-Newton matrix satisfies the secant condition, but does not have the same sparsity structure as the Hessian in general. Our numerical results demonstrate the usefulness of the new MCQN update with the BFGS formula for a collection of test problems. A local and superlinear convergence analysis is also provided for the new MCQN update with the DFP formula.

【 授权许可】

Unknown