论文标题
无约束多目标优化问题的可变度量方法
Variable Metric Method for Unconstrained Multiobjective Optimization Problems
论文作者
论文摘要
在本文中，我们提出了一种可变的度量方法，用于无约束的多目标优化问题（MOPS）。首先，使用通用框架中的不同正定矩阵生成一系列点。事实证明，序列的积累点是帕累托的临界点。然后，在没有凸度假设的情况下，为提出的方法建立了强收敛。此外，我们使用一个共同的矩阵来近似所有目标函数的Hessian矩阵，并提出了一种新的非单调线搜索技术来达到局部超级线性收敛速率。最后，几个数值结果证明了该方法的有效性。
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved that accumulation points of the sequence are Pareto critical points. Then, without convexity assumption, strong convergence is established for the proposed method. Moreover, we use a common matrix to approximate the Hessian matrices of all objective functions, along which, a new nonmonotone line search technique is proposed to achieve a local superlinear convergence rate. Finally, several numerical results demonstrate the effectiveness of the proposed method.
