非负约束稀疏优化问题的一个等价性条件

加权l₁最小化是稀疏优化的主流方法之一。本文对带非负约束的l₀最小化问题与加权l₁最小化问题的解之间的关系进行了研究，给出了加权l₁最小化问题的约束矩阵和目标函数的系数是"s-权优"的定义，并通过该定义给出了加权l₁最小化问题的解是带非负约束的l₀最小化问题的解的条件。进一步，本文给出了"s-权优"的充分条件及其具体表示形式，并对其上下界进行了可计算的有效估计。

An equivalence condition for sparse optimization problem with non-negative constraints

Weighted l₁ minimization is one of the mainstream methods for sparse optimization. Since the l₀ minimization problem is NP-hard, this paper studies the relationship between solutions of the l₀ minimization problem and the weighted l₁ minimization problem with non-negative constraints, and gives the definition of "s-weighted goodness" for the constraint matrix and the coefficient of the objective function. Through this definition, a sufficient condition is provided for a solution of the weighted l₁ minimization problem to be a solution of the l₀ minimization problem with non-negative constraints. Some results and proofs are provided from the perspective of monotonicity and robust stability. Further, this paper gives a sufficient condition for "s-weighted goodness", and shows lower and upper bounds of the sufficient condition, which are easy to check. Moreover, this paper also conducts an error analysis of the solution of the weighted l₁ minimization problem.