Analytical properties of the central path at boundary point in linear programming

We study the properties of the weighted central paths in linear programming. We consider each path as the function of the parameter μ ≥ 0 where the value at μ = 0 corresponds to the limit point at the boundary of the feasible set. We calculate the recursive formulas for the central path derivatives of all orders valid at each μ ≥ 0. We establish the geometric growth of the derivatives and, consequently, the analyticity of the weighted central path at μ ≥ 0. This paper also provides the analysis of limiting behavior of those projection operators which often appear in the interior point methods.