两个二维多参数绝对值优化问题解的等价性

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两个二维多参数绝对值优化问题解的等价性
Equivalence of Solutions for Two Two-Dimensional Multi-Parameter Absolute Value Optimization Problems

DOI: 10.12677/ORF.2023.132089, PDF, 下载: 107 浏览: 167
作者: 苑文丽, 张弦^*：贵州大学数学与统计学院，贵州贵阳
关键词: 最小一乘问题；l₀ 范数；MCP函数；多参数绝对值优化问题；解的等价性；Least Absolute Deviation； l₀ Norm； MCP Function； Multi-Parameter Absolute Value Optimization Problem； Equivalence of Solutions

摘要: 对带稀疏惩罚的最小一乘问题，采用MCP函数来连续松弛l₀函数，在二维情况下研究由此得到的两个多参数绝对值优化问题解的等价性。在简单条件下证明了两个问题具有相同全局最优解和最优值，为进一步研究相应高维问题提供了参考。

Abstract: In this paper, the MCP function is used to continuously relax the l₀ function for the least absolute deviation with sparse penalty, and the equivalence of the solutions of the two multi-parameter absolute value optimization problems is studied in two-dimensional space. Under simple conditions, it is proved that the two problems have the same global optimal solution and optimal value, which provides a reference for further study of the corresponding high-dimensional problems.

文章引用：苑文丽, 张弦. 两个二维多参数绝对值优化问题解的等价性[J]. 运筹与模糊学, 2023, 13(2): 859-876. https://doi.org/10.12677/ORF.2023.132089

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