Non-Convex Strong Duality Via Subdifferential

Abstract

In this article, the strong duality is treated. It is shown that the strong duality is equivalent to the non-emptiness of the subdifferential of a sort map involving the constraint functions. It is also noted that this technique is useful to verify the Assumption S. Indeed, the linearity of a constraint function h is not required as usually seen in the literature. Moreover, it is shown that this condition is easer to verify in the applications. We apply this new principle to the bi-obstacle problem, to the elastic-plastic torsion problem and to the continuum model of transportation.

Keywords:

• Bi-obstacle problem
• Continuum model of transportation
• Elastic-plastic problem
• Strong duality
• Subdifferential

Mathematics Subject Classification:

• 35J87
• 65K10
• 49N15

ACKNOWLEDGMENTS

The authors thank Prof. C. Zalinescu for useful conversations and suggestions about this topic and for the preprint [18].

Part of special issue, “Variational Analysis and Applications.”