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| Abstract: |
| Many methods have been put forward to solve unconstrained optimization problems, among which conjugate gradient method (CG) is very important. With the increasing emergence of large-scale problems, the subspace technology has become particularly important and widely used in the field of optimization. In this study, a new CG method was put forward, which combined subspace technology and a cubic regularization model. Besides, a special scaled norm in a cubic regularization model was analyzed. Under certain conditions, some significant characteristics of the search direction were given and the convergence of the algorithm was built. Numerical comparisons show that for the 145 test functions under the CUTEr library, the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods. |
| Key words: cubic regularization model conjugate gradient method subspace technique unconstrained optimization |
| DOI：10.11916/j.issn.1005-9113.2019066 |
| Clc Number:O221.2 |
| Fund: |
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| Descriptions in Chinese: |
| 基于三次正则模型的子空间极小化共轭梯度法 赵婷 ，刘红卫 （西安电子科技大学 数学与统计学院， 西安 710126） 共轭梯度法是求解无约束优化问题的一类主要方法，伴随着越来越多大规模问题的出现，子空间技术变得尤为重要，并且这种技术被广泛应用于最优化领域，本文通过在子空间上极小化当前迭代点处的三次正则化近似模型或者目标函数的二次近似模型来求解迭代方向，其中在三次正则模型中运用一种特殊的范数，结合非单调线搜索策略提出一个基于三次正则模型的子空间极小化共轭梯度算法。在一定条件下，证明搜索方向的两个重要性质，并给出算法的收敛性证明。数值结果表明本文所提算法具有良好的数值性能。 关键词：三次正则模型；共轭梯度法；子空间技术；无约束优化 |
