Abstract
We present an extension of Karmarkar's algorithm for solving a system of linear homogeneous equations on the simplex. It is shown that in at most O(nL) steps, the algorithm produces a feasible point or proves that the problem has no solution. The complexity is O(n 2 m 2 L) arithmetic operations. The algorithm is endowed with two new powerful stopping criteria.
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References
K.M. Anstreicher, “A monotonic projective algorithm for fractional linear programming,”Algorithmica 1 (1986) 483–498.
B. Apsvall and R.E. Stone, “Khachiyan's Linear Programming Algorithm,”Journal of Algorithms 1 (1980) 1–13.
G. de Ghellinck and J.-P. Vial, “A polynomial Newton method for linear programming,”Algorithmica 1 (1986) 425–453.
N. Karmarkar, “A new polynomial time algorithm for linear programming,”Combinatorica 4 (4) (1980) 373–395.
M.J. Todd and B.P. Burrell, “An extension of Karmarkar's algorithm for linear programming using dual variables,”Algorithmica 1 (1986) 409–424.
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de Ghellinck, G., Vial, J.P. An extension of Karmarkar's algorithm for solving a system of linear homogeneous equations on the simplex. Mathematical Programming 39, 79–92 (1987). https://doi.org/10.1007/BF02592072
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DOI: https://doi.org/10.1007/BF02592072