Averaged subgradient methods for constrained convex optimization and nash equilibria computation

Dan Butnariu, Elena Resmerita

Research output: Contribution to journalArticlepeer-review


We consider the problem of finding minima of convex functions under convex inequality constraints as well as the problem of finding Nash equilibria in n-person constant sum games. We prove that both problems can be solved by algorithms whose basic principles consist of representing the original problems as infinite systems of convex inequalities which, in turn, can be approached by outer projection techniques. Experiments showing how one of these algorithms behaves in test cases are presented and, in context, we describe a numerical method for computing subgradients of convex functions.

Original languageEnglish
Pages (from-to)863-888
Number of pages26
Issue number6
StatePublished - Dec 2002

Bibliographical note

Funding Information:
We wish to thank Professors M. Fukushima, R. Schultz and R. Tichatschke for interesting comments concerning the topics discussed in this article. Also, we are grateful to the referees for comments which helped to improve an earlier version of this article. Both authors gratefully acknowledge the support of the Israel Science Foundation founded by the Israel Academy of Science and Humanities


  • Constrained optimization problem
  • Nash equilibrium
  • Noncooperative n-person game
  • Subgradient

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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