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Minimax Theorems and Their Proofs

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Minimax and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 4))

Abstract

We suppose that X and Y are nonempty sets and f: X x Y →IR A minimax theorem is a theorem which asserts that, under certain conditions,

$$\mathop{{\min }}\limits_{Y} \mathop{{\max }}\limits_{X} f = \mathop{{\max }}\limits_{X} \mathop{{\min }}\limits_{Y} f.$$

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  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106-3080, USA

    Stephen Simons

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  1. University of Minnesota, USA

    Ding-Zhu Du

  2. Institute of Applied Mathematics, Beijing, China

    Ding-Zhu Du

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Simons, S. (1995). Minimax Theorems and Their Proofs. In: Du, DZ., Pardalos, P.M. (eds) Minimax and Applications. Nonconvex Optimization and Its Applications, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3557-3_1

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