A Lagrange multiplier theorem and a sandwich theorem for convex relations
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In this paper, the authors formulate and prove various separation principles for convex relations taking values in an order complete vector space, and these principles subsume the standard ones, and prove that these separation principles are optimal.Abstract:
We formulate and prove various separation principles for convex relations taking values in an order complete vector space. These principles subsume the standard ones.read more
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Book ChapterDOI
Theory of Vector Optimization
Christiane Tammer,Alfred Göpfert +1 more
TL;DR: This work derives necessary and sufficient optimality conditions, a minimal point theorem, a vector-valued variational principle of Ekeland’s type, Lagrangean multiplier rules and duality statements, and discusses a general scalarization procedure.
Book
Convex Functions: Constructions, Characterizations and Counterexamples
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A Duality Theory for Set-Valued Functions I: Fenchel Conjugation Theory
TL;DR: In this article, it was shown 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 set-valued affine minorants.
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Partially finite convex programming, part II: explicit lattice models
TL;DR: This work derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably, and shall apply its results to a number of more concrete problems, including variants of semi-infinite linear programming, L1 approximation, constrained approximation and interpolation, spectral estimation, semi-Infinite transportation problems and the generalized market area problem of Lowe and Hurter (1976).
References
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Journal ArticleDOI
Regularity and stability for the mathematical programming problem in Banach spaces
TL;DR: In this paper, a regularity assumption for the mathematical programming problem in Banach spaces is proposed, which is equivalent to the existence of a non-empty and weakly compact set of Lagrange multipliers.
Journal ArticleDOI
Regularity and Stability for Convex Multivalued Functions
TL;DR: Multivalued functions with convex graphs are shown to exhibit certain desirable regularity properties when their ranges have internal points to develop a perturbation theory for convex inequalities and to extend results on the continuity of convex functions.