Convex analysis and variational problems
Convex analysis and variational problems
Are dualities appropriate for duality theories in optimization?
Journal of Global Optimization
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We study conjugate duality with arbitrary coupling functions. Ouronly tool is a certain support property, which is automatically fulfilled inthe two most widely used special cases, namely the case where the underlyingspace is a topological vector space and the coupling functions are thecontinuous linear ones, and the case where the underlying space is a metricspace and the coupling functions are the continuous ones. We obtain therebya simultaneous axiomatic extension of these two classical models. Alsoincluded is a condition for global optimality, which requires only thementioned support property.