ABSTRACT

P= {x ∈ Rn : Ax = b, x≥ 0}, (8.2) where A ∈ Rm×n and b ∈ Rm are given. We assume that m < n, b = 0 and P = ∅ throughout this chapter. Under this assumption we see that 0 /∈ P. We also generalize the algorithm for the above problem to an underdetermined system of linear equations without non-negative constraints. The algorithms discussed in this chapter can be called the reweighted 1-algorithms via dual density. These algorithms are remarkably different from the traditional reweighted 1-algorithms presented in Chapter 7.