An estimate of Lagrange multipliers for linear programming using interior point methods (Q1202824)

A linear programming problem with inequality constraints is considered: \(\max b^ T y\) subject to \(A^ T y\leq c\). Assume that the feasible region of the constraints is of a bounded full-dimensional polytope, and the optimal solution of the problem is nondegenerate. A high-order estimation formula of Lagrange multipliers is set up in the neighborhood of the optimal solution as a sequence generated by using the center point method approaches to the solution. It is very useful for reaching an approximate optimal solution with high-order precision.