Convergence of the CA algorithm for nonlinear programs

  • Michael Patriksson
Part of the Applied Optimization book series (APOP, volume 23)

Abstract

Theorem 5.1 (Convergence under Rule E). Assume that u is continuous on dom u∩X. Let the sequencet} of cost approximating mappings be constructed such that, for each t, either Φt := Φ(,xt) for a given mapping Φ : (dom u∩X) x (dom u∩X) ↦ Rn of the form Φ(y,x), continuous on (dom u∩X) x (dom u∩X) and maximal and strictly monotone on dom u∩X with respect to y, or Φt := ∇φ(, xt) for a given function φ : (dom u∩X) x (dom u∩X) ↦ R of the form φ(y,x), continuous on (dom u∩X) x (dom u∩X) and convex and in C1 on dom u∩X with respect to y.

Keywords

Step Length Line Search Accumulation Point Nonlinear Program Variational Inequality Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Michael Patriksson
    • 1
  1. 1.Chalmers University of TechnologyGothenburgSweden

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