Abstract
Based on the recently developed ABS algorithm for solving linear Diophantine equations, we present a special ABS algorithm for solving such equations which is effective in computation and storage, not requiring the computation of the greatest common divisor. A class of equations always solvable in integers is identified. Using this result, we discuss the ILP problem with upper and lower bounds on the variables.
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Mei-feng Zou is a M. D candidate of Dalian University of Technology under the direction of Prof. Zun-Quan Xia. Her research interests is in the theory and application of the ABS algorithms.
Zun-Quan Xia is a professor in Department of Applied Mathematics, DUT, Dalian, China. He graduated from Fudan University, Shanghai, as a graduate student in 1968. His research areas are (smooth, nonsmooth, discrete and numerical) optimization, OR methods and applications.
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Zou, MF., Xia, ZQ. ABS algorithms for Diophantine linear equations and integer LP problems. JAMC 17, 93–107 (2005). https://doi.org/10.1007/BF02936043
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DOI: https://doi.org/10.1007/BF02936043