Convex Sets and Convex Programming

  • A. V. Balakrishnan


In this chapter we concentrate on properties of convex sets in a Hilbert space and some of the related problems of importance in application to convex programming: variational problems for convex functions over convex sets, central to which are the Kuhn-Tucker theorem and the minimax theorem of von Neumann, which in turn are based on the “separation” theorems for convex sets. A related result is the Farkas lemma in finite dimensions which finds application in network flow problems.


Hilbert Space Boundary Point Interior Point Convex Program Positive Cone 
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Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • A. V. Balakrishnan
    • 1
  1. 1.Systems Science DepartmentUniversity of CaliforniaLos AngelesUSA

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