Abstract
We study conjugate duality with arbitrary coupling functions. Our only tool is a certain support property, which is automatically fulfilled in the two most widely used special cases, namely the case where the underlying space is a topological vector space and the coupling functions are the continuous linear ones, and the case where the underlying space is a metric space and the coupling functions are the continuous ones. We obtain thereby a simultaneous axiomatic extension of these two classical models. Also included is a condition for global optimality, which requires only the mentioned support property.
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Oettli, W., Schläger, D. Conjugate Functions for Convex and Nonconvex Duality. Journal of Global Optimization 13, 337–347 (1998). https://doi.org/10.1023/A:1008300205223
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DOI: https://doi.org/10.1023/A:1008300205223