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

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.


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
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