Generalized concavity and duality with a square root term

Abstract

Duality results for a class of nondifferentiable mathematical programming problems are given. These results allow for the weakening of the usual convexity conditions required for duality to hold. A pair of symmetric and self dual nondifferentiable programs under weaker convexity conditions are also given. A subgradient symmetric duality is proposed and its limitations discussed. Finally, a pair of nondifferentiable mathematical programs containing arbitrary norms is presented.

Keywords:

• Nondifferentiable mathematical programming
• duality

AMS 1980 Subject Classifications:

• Primary: 90 C 3
• Secondary: 49 B 27

¹Research by this author was carried out while he was a visiting research fellow at the University of Melbourne

¹Research by this author was carried out while he was a visiting research fellow at the University of Melbourne

Notes

¹Research by this author was carried out while he was a visiting research fellow at the University of Melbourne