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Since Karmarkar's projective algorithm, many interior point methods for linear programming problem have been proposed. This paper presents a primal affine scaling algorithm for linear programming problem with bounded variables. This algorithm is derived from the standard affine scaling algorithm, separating the equality constraints about the bounded variables with the added slack variables. An implementation detail of this algorithm is also described. A program code based on this algorithm is developed using sparse matrix data structures, and applied to utility plant optimization problem. Numerical examples show that the proposed algorithm is practical for industrial plant optimization problem, and much superior in computing time to the standard primal affine scaling algorithm.

An Affine Scaling Algorithm for Linear Programming Problem and its Application to Utility Plant Optimization