Classical minimax theory initiated by Von Neumann, together with duality and saddle point analysis, has played a critical role in optimization and game theory. However, minimax problems and techniques appear in a very wide area of disciplines. There are many interesting and sophisticated problems formulated as minimax problems. For example, many combinatorial optimization problems, including scheduling, location, allocation, packing, searching, and triangulation, can be represented as a minimax problem. Many of these problems have nothing to do with duality and saddle points, and they have not been considered in any general uniform treatment. Furthermore, many minimax problems have deep mathematical background, nice generalizations, and lead to new areas of research in combinatorial optimization. In this survey, we discuss a small but diverse collection of minimax problems, and we present some results (with a few key references) and open questions.
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