多目标基数约束优化问题的惩罚分解方法

M. Lapucci
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引用次数: 3

摘要

在这篇文章中,我们考虑了决策变量向量上的基数约束和附加线性约束的多目标优化问题。对于这类问题,我们分析了帕累托最优的充分必要条件。随后,我们提出了一种惩罚分解型算法,利用多目标下降方法来解决上述问题。我们对所提出的方法进行了严格的收敛性分析,证明了所产生的点序列有极限点,每个点都是可行的,并且满足一阶最优性条件。对稀疏均值/方差组合选择和稀疏正则化逻辑回归等现实问题的多目标公式进行了数值计算实验,结果表明,本文提出的方法能够有效地找到形成良好Pareto集近似的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A penalty decomposition approach for multi-objective cardinality-constrained optimization problems
In this manuscript, we consider multi-objective optimization problems with a cardinality constraint on the vector of decision variables and additional linear constraints. For this class of problems, we analyse necessary and sufficient conditions of Pareto optimality. We afterwards propose a Penalty Decomposition type algorithm, exploiting multi-objective descent methods, to tackle the aforementioned family of problems. We conduct a rigorous convergence analysis for the proposed method, where we prove that the produced sequence of points has limit points, each one being feasible and satisfying first-order optimality conditions. Numerical computational experiments, carried out on instances of relevant real-world problems such as sparse mean/variance portfolio selection and sparse regularized logistic regression, in their multi-objective formulation, show that the proposed procedure is effective at finding solutions forming good Pareto sets approximations.
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