Equivalence of the two-curve de la Vallée-Poussin procedure and the dual simplex method

Consider the two-curve Chebyshev approximation problem and its corresponding linear programming formulation. The de la Vallée-Poussin procedure is an iterative procedure for finding the Chebyshev approximation by updating a basis of maximal deviation points. Equivalence conjecture. The two-curve approximation de la Vallée-Poussin's procedure is equivalent to the dual simplex method applied to the corresponding linear programming problem. Establishing this equivalence would connect the approximation procedure with a standard optimization algorithm and may clarify its computational properties. The paper identifies this as a future research direction; no resolution is given.