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Global and approximate optimization for constrained max-min systems
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DOI：10.1016/j.fss.2025.109654.png)
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Abstract
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This paper focuses on the global optimization problem in max-min systems subject to non-negative affine equality constraints. By constructing the greatest lower bound, we establish a solvability criterion for the global optimization problem and derive a uniqueness criterion for globally optimal solutions. We construct the feasible max-plus projection set to determine the set of all globally optimal solutions. An algorithm is developed to verify the solvability of the global optimization problem and to find all globally optimal solutions. Furthermore, when the global optimization problem is unsolvable, we introduce approximate optimization to obtain the optimal feasible value by using the max-plus vector norm, and provide the set of all approximate optimal solutions. The effectiveness of the proposed method is demonstrated through illustrative examples.
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