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A Minimal Point Theorem in Uniform Spaces
(Kluwer Academic Publishers, 2003)We present a minimal point theorem in a product space X × Y , X being a separated uniform space, Y a topological vector space under the weakest assumptions up to now. We state Ekeland’s variational prin ciple and ... 
Minimal element theorems and Ekeland's principle with set relations
(YOKOHAMA PUBL, 2006)We present two existence principles for minimal points of subsets of the product space X × 2Y, where X stands for a separated uniform space and Y a topological vector space. The two principles are distinct with respect to ... 
Minimal elements for product orders
(2008)The aim of the present article is to generalize several results of 19 for product spaces X × V, where X is a complete metric space and V is a Banach space and to give considerably simplified proofs. Moreover, we discuss ... 
Phelps’ Lemma, Danes’ Drop theorem and Ekeland’s principle in locally convex spaces
(2003)A generalization of Phelps' lemma to locally convex spaces is proven, applying its wellknown Banach space version. We show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex ... 
Equivalents to Ekeland’s variational principle in uniform spaces
(Elsevier, 2005)A minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of [Pacific J. Math. 55(2) (1974) 335–341; Proc. Amer. Math. Soc. 108(3) (1990) 707–714]. Two more equivalent ... 
Closing the duality gap in linear vector optimization
(2004)Using a setvalued dual cost function we give a new approach to duality theory for linear vector optimization problems. We develop the theory very close to the scalar case. Especially, in contrast to known results, we avoid ... 
A duality theory for setvalued functions I: Fenchel conjugation theory
(SPRINGER, 2009)It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space is the pointwise supremum of its setvalued affine minorants. A new concept of LegendreFenchel ... 
An εlagrange multiplier rule for a mathematical programming problem on Banach spaces
(2001)The aim of this paper is to extend the multiplier rule due to Clarke for a nondifferentiable mathematical programming problem on a Banach space to eminimal (suboptimal) solutions of the problem. This seems to be useful ...