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<p>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.</p>
linear programming; primal-dual interior-point method; optimization; Newton's method; nonlinear equations; Joseph Lagrange's methods; equality constraints; inequality constraints; linear programming
Greg Astfalk, Irvin Lustig, Roy Marsten, David Shanno, "The Interior-Point Method for Linear Programming", IEEE Software, vol. 9, no. , pp. 61-68, July/August 1992, doi:10.1109/52.143109
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