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Are dualities appropriate for duality theories in optimization?

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Abstract

We raise some questions about duality theories in global optimization. The main one concerns the possibility to extend the use of conjugacies to general dualities for studying dual optimization problems. In fact, we examine whether dualities are the most general concepts to get duality results. We also consider the passage from a Lagrangian approach to a perturbational approach and the reverse passage in the framework of general dualities. Since a notion of subdifferential can be defined for any duality, it is natural to examine whether the familiar interpretation of multipliers as generalized derivatives of the performance function associated with a dualizing parameterization of the given problem is still valid in the general framework of dualities.

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  1. Laboratoire de Mathématiques, CNRS UMR 5142, Faculté des Sciences, Université de Pau, B.P. 1155, 64013, Pau cedex, France

    Jean-Paul Penot

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Penot, JP. Are dualities appropriate for duality theories in optimization?. J Glob Optim 47, 503–525 (2010). https://doi.org/10.1007/s10898-009-9478-z

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