Journal of Optimization Theory and Applications

, Volume 71, Issue 3, pp 517–534 | Cite as

The generalized order complementarity problem

  • G. Isac
  • M. Kostreva
Contributed Papers


Given an ordered Banach Space (E,K) andm functionsf1,f2,...,fm:EE, the generalized order complementarity problem associated with {fi} andK is to findx0K such thatfi(x0)∈K,i=1,...,m, and Λ (x0,f1(x0),...,fm(x0))=0. The problem is shown to be equivalent to several fixed-point problems and equivalent to the order complementarity problem studied by Borwein and Dempster and by Isac. Existence and uniqueness of solutions and least-element theory are shown in the spacesC(Ω, ℝ) andLp(Ω, μ). For general locally convex spaces, least-element theory is derived, existence is proved, and an algorithm for computing a solution is presented. Applications to the mixed lubrication theory of fluid mechanics are described.

Key Words

Complementarity ordered spaces fixed points lubrication theory 


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • G. Isac
    • 1
  • M. Kostreva
    • 2
  1. 1.Départment de MathématiquesCollège Militaire Royal de Saint-JeanCanada
  2. 2.Department of Mathematical SciencesClemson UniversityClemson

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