A Barzilai-Borwein descent method for multiobjective optimization problems
A Barzilai-Borwein descent method for multiobjective optimization problems
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DOI：
10.1016/j.ejor.2023.04.022
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Jian Chen;L. Tang;Xinmin Yang
中科院分区：
文献类型：
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作者：
Jian Chen;L. Tang;Xinmin Yang
Fliege和Svaiter提出的最速下降法激发了多目标优化下降法的研究，近年来受到越来越多的关注。然而，实验结果表明，Armijo线搜索往往会导致一个非常小的步长沿着最陡下降方向，这严重减慢收敛。本文指出，这主要是由于目标函数之间的不平衡。为了解决这个问题，我们提出了一个Barzilai-Borwein下降法多目标优化（BBDMO），动态调谐梯度幅度使用Barzilai-Borwein的规则在测向子问题。我们强调，BBDMO产生一个序列的新的下降方向相比，Barzilai-Borwein的方法提出的Morovati等人。利用单调和非单调线搜索技术，证明了BBDMO算法生成的聚点是Pareto临界点。理论结果表明，在BBDMO算法中，Armijo线搜索可以获得更好的搜索步长.最后，数值实验的比较结果报告，说明BBDMO的效率和验证的理论结果。
The steepest descent method proposed by Fliege and Svaiter has motivated the research on descent methods for multiobjective optimization, which has received increasing attention in recent years. However, empirical results show that the Armijo line search often results in a very small stepsize along the steepest descent direction, which decelerates the convergence seriously. This paper points out the issue is mainly due to imbalances among objective functions. To address this issue, we propose a Barzilai-Borwein descent method for multiobjective optimization (BBDMO), which dynamically tunes gradient magnitudes using Barzilai-Borwein’s rule in direction-finding subproblem. We emphasize that the BBDMO produces a sequence of new descent directions compared to Barzilai-Borwein’s method proposed by Morovati et al. With monotone and nonmonotone line search techniques, we prove that accumulation points generated by BBDMO are Pareto critical points, respectively. Furthermore, theoretical results indicate that the Armijo line search can achieve a better stepsize in BBDMO. Finally, comparative results of numerical experiments are reported to illustrate the efficiency of BBDMO and verify the theoretical results.