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Support functions and subdifferentials

Grzybowski J., Pallaschke D., Urbański R.

Commentationes Mathematicae

2016

Vol 56, No. 1

45--53

In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.

Efficiency and duality for generalized convex multiobjective programming

Yan Z.-X.

Journal of Applied Analysis

2008

Vol. 14, nr 1

63-71

Under a class of generalized (Type I, F, ρ)-convexity assumptions, the author formulates the sufficient conditions about Pareto efficiency and Geoffrion proper efficiency and gets the dual results between multiobjective programming and its Wolfe dual.

Sublinear Functionals and Weak - compatness

Ger R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2005

Vol. 10

67--76

Let X be a real locally convex linear topological space. A functional f : X → lR is called sublinear provided that f is subadditive and f(nx) = nf(x),x ∈ X,n ∈ IN. We establish a one-to-one correspondence between the collectron of all sublinear functional satisfying some mild regularity conditions and the family of all nonempty convex and weakly"- compact subsets of the dual space X*.