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Boccuto, Antonio

Hahn-Banach-type theorems and subdifferentials for invariant and equivariant order continuous vector lattice-valued operators with applications to optimization. (English) Zbl 1491.46074

Tatra Mt. Math. Publ. 78, 139-156 (2021).
Summary: We give some versions of Hahn-Banach, sandwich, duality, Moreau-Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group \(G\) of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

MSC:

46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
28B15 Set functions, measures and integrals with values in ordered spaces
43A07 Means on groups, semigroups, etc.; amenable groups
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49K27 Optimality conditions for problems in abstract spaces

Keywords:

vector lattice; order bounded functional; order continuous functional; amenability; Hahn-Banach theorem; sandwich theorem; Fenchel duality theorem; subgradient; subdifferential of composite functions; optimality condition; Moreau-Rockafellar formula; Farkas theorem; Kuhn-Tucker theorem
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