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Hahn-Banach-type theorems and applications to optimization for partially ordered vector space-valued invariant operators. (English) Zbl 1444.46003

The author inspects the natural extensions of subdifferential calculus in the environment of invariance, Dedekind complete ranges, amenability, and nonempty interior. Applications are given to the standard toolkit of abstract optimization.

MSC:

46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46A40 Ordered topological linear spaces, vector lattices
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
28B15 Set functions, measures and integrals with values in ordered spaces
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References:

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