The interior-point method for linear programming

A robust, reliable, and efficient implementation of the primal-dual interior-point method for linear programs, which is based on three well-established optimization algorithms, is presented. The authors discuss the theoretical foundation for interior-point methods which consists of three crucial building blocks: Newton's method for solving nonlinear equations, Joseph Lagrange's methods for optimization with equality constraints, and Fiacco and McCormick's barrier method for optimization with inequality constraints. The construction of the primal-dual interior-point method using these methods is described. An implementation of the primal-dual interior-point method, its performance, and a comparison to other interior-point methods are also presented.>