Max Plus Algebra, Optimization and Game Theory

  • Dipti Dubey
  • S. K. NeogyEmail author
  • Sagnik Sinha
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


Max-plus algebra has been applied to several fields like matrix algebra, cryptography, transportation, manufacturing, information technology and study of discrete event systems like subway traffic networks, parallel processing systems, telecommunication networks for many years. In this paper, we discuss various optimization problem using methods based on max-plus algebra, which has maximization and addition as its basic arithmetic operations. We present some sub-classes of mathematical optimization problems like linear programming, convex quadratic programming problem, fractional programming problem, bimatrix game problem and some classes of stochastic game problem in max algebraic framework and discuss various connections between max-plus algebra and optimization.


Max-plus algebra Linear programming Convex quadratic programming problem Fractional programming problem Bimatrix game problem 



The authors would like to thank the anonymous referees for their constructive suggestions which considerably improve the overall presentation of the paper. The authors would like to thank Professor R. B. Bapat, Indian Statistical Institute, Delhi Centre for his valuable comments and suggestions. The first author wants to thank the Science and Engineering Research Board, Department of Science & Technology, Government of India, for financial support for this research.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Statistical InstituteNew DelhiIndia
  2. 2.Jadavpur UniversityKolkataIndia

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