Abstract
This paper proposes an unconstrained dual approach and an efficient algorithm for solving Karmarkar-type linear programming problems. Conventional barrier functions are incorporated as a perturbation term in the derivation of the associated duality theory. An optimal solution of the original linear program can be obtained by solving a sequence of unconstrained concave programs, or be approximated by solving one such dual program with a sufficiently small perturbation parameter. A globally convergent curved-search algorithm with a quadratic rate of convergence is designed for this purpose. Based on our testing results, we find that the computational procedure is very efficient and can be a viable approach for solving linear programming problems.
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Jacob Tsao, H.S., Fang, SC. An unconstrained dual approach to solving Karmarkar-type linear programs using conventional barrier functions. ZOR - Methods and Models of Operations Research 42, 325–343 (1995). https://doi.org/10.1007/BF01432508
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DOI: https://doi.org/10.1007/BF01432508