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Maximization of lower semi-continuous convex functional on bounded subsets of locally convex spaces. II: Quasi-Lagrangian duality theorems

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Abstract

We prove, for a proper lower semi-continuous convex functional ƒ on a locally convex space E and a bounded subset G of E, a formula for sup ƒ(G) which is symmetric to the Lagrange multiplier theorem for convex minimization, obtained in [7], with the difference that for sup ƒ(G) Lagrange multiplier functionals need not exist. When ƒ is also continuous we give some necessary conditions for g0 ∈ G to satisfy ƒ(g0) = sup ƒ(G). Also, we give some applications to deviations and farthest points. Finally, we show the connections with the “hyperplane theorems” of our previous paper [8].

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References

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  1. National Institute for Scientific and Technical Creation and Institute of Mathematics, Bucharest, Romania

    Ivan Singer

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  1. Ivan Singer
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Singer, I. Maximization of lower semi-continuous convex functional on bounded subsets of locally convex spaces. II: Quasi-Lagrangian duality theorems. Results. Math. 3, 235–248 (1980). https://doi.org/10.1007/BF03323359

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  • DOI: https://doi.org/10.1007/BF03323359

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