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解非线性规划的组合同伦JFNG内点算法
发表时间：2012-01-15 浏览量：2110 下载量：629
| 全部作者： | 王斌，于波 |
| 作者单位： | 大连理工大学数学科学学院 |
| 摘 要： | 以组合同伦内点(combined homotopy interior point, CHIP)算法为例，采用割线预估的同时，将Jacobian-Free Newton-GMRES(JFNG)方法应用于占据数值同伦方法主要计算量的校正步，作为其非线性方程组的求解器，给出基于JFNG方法的数值同伦方法，以此改进传统Newton-PLU方法在同伦算法校正阶段所出现的如“过解”等计算效率低下的弊端。在CUTEr测试库中所进行的数值实验结果充分表明改进后的同伦算法效率获得明显提升。 |
| 关 键 词： | 非线性规划；组合同伦内点算法；非精确牛顿法；PLU分解；Jacobian-Free Newton-GMRES；CUTEr |
| Title： | Combined homotopy method with JFNG for solving nonlinear programming |
| Author： | WANG Bin, YU Bo |
| Organization： | School of Mathematical Sciences, Dalian University of Technology |
| Abstract： | This paper brings Jacobian-Free Newton-GMRES (JFNG) method as the solver for the nonlinear equations into the homotopy methods which are selected as combined homotopy interior point (CHIP) with the secant prediction, aiming to eliminate some drawbacks of the low efficiency such as “excessively solving” caused by traditional Newton-PLU method in the corrector phase of the path tracking process. The numerical experiments conducted under CUTEr environment fully demonstrate that the execution efficiencies of the improved homotopy methods have been greatly improved. |
| Key words： | nonlinear programming; combined homotopy; inexact Newton method; PLU decomposition; Jacobian-Free Newton-GMRES; CUTEr |
| 发表期数： | 2012年1月第1期 |
| 引用格式： | 王斌，于波. 解非线性规划的组合同伦JFNG内点算法[J]. 中国科技论文在线精品论文，2012，5（1）：12-17. |
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