Globally optimal solutions of max---min systems

Authors:
Yuegang Tao;Guo-Ping Liu;Wende Chen
Affiliations:
Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing, Peoples Republic of China 100080;Department of Engineering, University of Glamorgan, Pontypridd, UK CF37 1DL and Laboratory of Networked Control Systems, Central South University, Changsha, Peoples Republic of China 410083;Laboratory of Networked Control Systems, Central South University, Changsha, Peoples Republic of China 410083
Venue:
Journal of Global Optimization
Year:
2007

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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.