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Efficiency and duality for generalized convex multiobjective programming

100%

Yan Z.-X.

Journal of Applied Analysis

2008

tom 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

100%

Ger R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2005

tom 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*.

Some remarks on the space of differences of sublinear functions

100%

Bartels S. G. , Pallaschke D.

Applicationes Mathematicae

1993-1995

tom 22

nr 3

419-426

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of the farthest point mapping to its subdifferential at the origin. This leads to a simple family of sublinear functions which contains an exhaustive family of upper convex approximations for any quasidifferentiable function.

Support functions and subdifferentials

88%

Grzybowski J. , Pallaschke D. , Urbański R.

Commentationes Mathematicae

2016

tom 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.

Classifications and existence of positive solutions of a higher order nonlinear difference equation

88%

Li W.-T. , Cheng S. S.

Colloquium Mathematicum

2000

tom 83

nr 1

137-153

A classification scheme for the eventually positive solutions of a class of higher order nonlinear difference equations is given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of such solutions are provided.

Support functions and subdifferentials

88%

Grzybowski J. , Pallaschke D. , Urbański R.

tom 56

nr 1

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.