Characterizations of optimality without constraint qualification for the abstract convex program

  • J. M. Borwein
  • H. Wolkowicz
Part of the Mathematical Programming Studies book series (MATHPROGRAMM, volume 19)


We consider the general abstract convex program (P) minimize f(x), subject to g(x)∈−S, where f is an extended convex functional on X, g: X→Y is S-convex, S is a closed convex cone and X and Y are topological linear spaces. We present primal and dual characterizations for (P). These characterizations are derived by reducing the problem to a standard Lagrange multiplier problem. Examples given include operator constrained problems as well as semi-infinite programming problems.

Key words

Cone-convex Locally Convex Topological Vector Space Optimality Conditions Subdifferential Directional Derivative Faithfully Convex Lagrange Multipliers Slater’s Condition Semi-infinite Programs 


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Copyright information

© The Mathematical Programming Society, Inc. 1982

Authors and Affiliations

  • J. M. Borwein
    • 1
  • H. Wolkowicz
    • 1
  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada

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