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Optimality conditions using sum-convex approximations

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Abstract

The purpose of this paper is to give necessary and sufficient conditions of optimality for a general mathematical programming problem, using not a linear approximation to the constraint function but an approximation possessing certain convexity properties. Such approximations are called sum-convex. Theorems of the alternative involving sum-convex functions are also presented as part of the proof.

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Additional information

This work is part of the author's PhD Thesis under the supervision of Professor S. Zlobec at McGill University.

Communicated by M. Avriel

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Massam, H. Optimality conditions using sum-convex approximations. J Optim Theory Appl 35, 475–495 (1981). https://doi.org/10.1007/BF00934928

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Key Words

  • Mathematical programming
  • convex approximations
  • theorems of the alternative
  • optimality conditions