On Min-Max Optimization of a Collection of Classical Discrete Optimization Problems
In this paper, we study discrete optimization problems with min-max objective functions. This type of optimization has long been the attention of researchers, and it has direct applications in the recent development of robust optimization. The following well-known classes of problems are discussed: 1) the minimum spanning tree problem, 2) the resource allocation problem with separable cost functions, and 3) the production control problem. Computational complexities of the corresponding min-max version of the above-mentioned problems are analyzed. Pseudo-polynomial algorithms for these problems under certain conditions are provided.
KeywordsSpan Tree Robust Optimization Resource Allocation Problem Discrete Optimization Problem Grid Graph
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