Abstract
A variety of problems in computer science, operations research, control theory, etc., can be modeled as non-linear and non-differentiable max–min systems. This paper introduces the global optimization into such systems. The criteria for the existence and uniqueness of the globally optimal solutions are established using the high matrix, optimal max-only projection set and k s-control vector of max–min functions. It is also shown that the global optimization can be accomplished through the partial max-only projection representation with algebraic and combinatorial features. The methods are constructive and lead to an algorithm of finding all globally optimal solutions.
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Tao, Y., Liu, GP. & Chen, W. Globally optimal solutions of max–min systems. J Glob Optim 39, 347–363 (2007). https://doi.org/10.1007/s10898-007-9141-5
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DOI: https://doi.org/10.1007/s10898-007-9141-5