Multiplier rules and the separation of convex sets

  • B. H. Pourciau
Contributed Papers


We consider the following abstract mathematical programming problem: in a setD, find an element that optimizes a real function φ0, subject to inequality constraints φ1⩽0, ..., φ p ⩽0 and equality constraints φp+1=0, ..., φ p+q =0. Necessary conditions for this problem, like the Karush-Kuhn-Tucker theorem, can be seen as a consequence of separating with a hyperplane two convex sets inRp+q+1, the image space of the map Φ=(φ0, φ1, ..., φ p+q ). This paper reviews this approach and organizes it into a coherent way of looking at necessary conditions in optimization theory.

Key Words

Optimization necessary conditions Kuhn-Tucker theorem multiplier rules separation of convex sets mathematical programming generalized derivatives 


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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • B. H. Pourciau
    • 1
  1. 1.Department of MathematicsLawrence UniversityAppleton

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