Nested monotony for variational inequalities over product of spaces and convergence of iterative algorithms

G. Cohen, F. Chaplais

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The auxiliary problem principle has been proposed by the first author as a framework to describe and analyze iterative algorithms such as gradient as well as decomposition/coordination algorithms for optimization problems (Refs. 1-3) and variational inequalities (Ref. 4). The key assumption to prove the global and strong convergence of such algorithms, as well as of most of the other algorithms proposed in the literature, is the strong monotony of the operator involved in the variational inequalities. In this paper, we consider variational inequalities defined over a product of spaces and we introduce a new property of strong nested monotony, which is weaker than the ordinary overall strong monotony generally assumed. In some sense, this new concept seems to be a minimal requirement to insure convergence of the algorithms alluded to above. A convergence theorem based on this weaker assumption is given. Application of this result to the computation of Nash equilibria can be found in another paper (Ref. 5).

Original languageEnglish
Pages (from-to)369-390
Number of pages22
JournalJournal of Optimization Theory and Applications
Issue number3
StatePublished - 1 Dec 1988
Externally publishedYes


  • Monotony
  • convergence of algorithms
  • coordination algorithms
  • decomposition
  • optimization problems
  • variational inequalities

ASJC Scopus subject areas

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


Dive into the research topics of 'Nested monotony for variational inequalities over product of spaces and convergence of iterative algorithms'. Together they form a unique fingerprint.

Cite this