Chebyshev approximations do not need the Haar condition

In this paper, we consider the problem of constructing a Chebyshev projection of the coordinate origin onto a linear manifold. In particular, the Chebyshev linear approximation problem can be formulated in this form. We present an algorithm for determining Chebyshev projections, which is not based on the Haar condition. The algorithm consists of finding relatively interior points of optimal solutions of a finite sequence of linear programming problems.