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

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。

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.