Free disposal hull condition to verify when efficiency coincides with weak efficiency
Free disposal hull condition to verify when efficiency coincides with weak efficiency
复制标题
自由处置船体状况以验证何时效率与弱效率一致
DOI：
10.1007/s10957-021-01961-5
复制
发表时间：
2022
影响因子：
1.9
通讯作者：
Shunsuke
中科院分区：
文献类型：
--
作者：
Hamada;Naoki; Ichiki;Shunsuke
在用标量化技术求解多目标优化问题时，标量化问题的解一般是弱有效的，而不是原问题的有效解。因此，关键是要了解什么条件确保所有弱有效解都是有效的。在给定集合的自由处置船体是凸的条件下，给出了有效性与弱有效性一致的一个条件。利用这一特征，我们得到了各种应用的多目标优化问题在某些凸条件下。我们还将主要定理应用于最小绝对收缩和选择算子（LASSO），并表明对于多目标版本的LASSO，所有弱有效的解决方案是有效的。数值模拟表明，这种等价性有助于加速LASSO的超参数搜索。
In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what condition ensures that all weakly efficient solutions are efficient. In this paper, we give a condition to verify when efficiency coincides with weak efficiency, provided that the free disposal hull of a given set is convex. By using this characterization, we obtain various applications to multi-objective optimization problems under some convex conditions. We also apply the main theorem to the least absolute shrinkage and selection operator (LASSO) and show that for a multi-objective version of LASSO, all weakly efficient solutions are efficient. Numerical simulation demonstrates that this equivalence is helpful to accelerate the hyper-parameter search for LASSO.