| 王菲菲,徐尔,赵金玲.一种基于四阶Taylor展开的多目标改进的拟牛顿算法研究[J].井冈山大学自然版,2016,(1):26-28 |
| 一种基于四阶Taylor展开的多目标改进的拟牛顿算法研究 |
| NEW QUASI-NEWTON'S METHOD BASED ON FOUR-ORDER TAYLOR SERIES EXPANSION FOR MULTIOBJECTIVE OPTIMIZATION |
| 投稿时间：2015-10-06 修订日期：2015-12-20 |
| DOI：10.3969/j.issn.1674-8085.2016.01.006 |
| 中文关键词: 多目标优化 四阶Taylor展开 M-TBFGS方法 Wolfe线搜索 Pareto最优解 |
| 英文关键词: multiobjective optimization four-order Taylor series expansion M-TBFGS method Wolfe line search Pareto optimal |
| 基金项目:国家自然科学基金青年基金项目(11101028);北京高校青年英才计划项目(YETP0385) |
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| 中文摘要: |
| 借助于目标函数的四阶Taylor展开导出新的拟牛顿方程,并将其应用到多目标优化问题中,给出了一种多目标优化改进的拟牛顿算法(称为M-TBFGS算法),同时在一定的假设条件下,结合Wolfe搜索准则,证明了本文算法的收敛性,并进行了数值试验,结果表明,本文的M-TBFGS算法是正确和有效的。 |
| 英文摘要: |
| The new quasi-Newton's equation is applied to multiobjective optimization, which is derived by using the four-order Taylor series expansion. The improved method for multiobjective optimization without constraints is presented, which is called M-TBFGS algorithm. Furthermore, its global convergence is proved. Under the Wolfe line search, numerical results also show that the proposed method is correct and efficient. |
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