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An algorithm for minimax

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Abstract

An algorithm is proposed for computing an unconstrained minimax, based on differential equations with suitable stabilization terms. Methods for accelerating the convergence are discussed. For computing a constrained minimax, the augmented Lagrangian algorithm of Powell, Hestenes and Rockafellar is generalized to minimax, assuming the unconstrained minimax algorithm as a subroutine. An estimate of the convergence rate is obtained.

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References

  1. Auslender A (1972) Problèmes de minimax via l'analyse convexe et les inégalités variationelles: théorie et algorithms. Lecture Notes in Economies and Math. Systems 77. Springer, Berlin

    Google Scholar 

  2. Bellman R (1953) Stability theory of differential equations. Dover, New York

    Google Scholar 

  3. Bertsekas DP (1982) Constrained optimization and Lagrange multipliers. Academic Press, New York

    Google Scholar 

  4. Dem'janov VF (1967) Successive approximations for finding saddle points. Soviet Math Dokl8(6): 1350–1353

    Google Scholar 

  5. Goh CJ, Teo KL (1987) MISER, an optimal control software. Dept of Industrial Engineering. National University of Singapore

  6. Hartung J (1982) An extension of Sion's minimax theorem with an application to a method for constrained games. Pac J Math 103:401–408

    Google Scholar 

  7. Shimizu KA, Amoshi E (1980) Necessary condition for min-max problems and algorithms by a relaxation procedure. IEEE Trans on Automatic Control, AC-25:62–66

    Google Scholar 

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Craven, B.D. An algorithm for minimax. ZOR - Methods and Models of Operations Research 35, 425–434 (1991). https://doi.org/10.1007/BF01498333

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  • DOI: https://doi.org/10.1007/BF01498333

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