A DIRECT SEARCH FRAME-BASED CONJUGATE GRADIENTS METHOD

• 来源期刊: 计算数学(英文版)
• 关键词: Conjugate gradients Derivative-free Frame-based methods Numerical results.
• 年，卷（期）: 2004,（4）
• 页码范围: 489-500
• 页数: 12页
• 语种: 英文

摘要

A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for C1 functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasiNewton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.