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Some characterizations of surrogate dual problems
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For constrained primal infimization problems, some characterizations of the surrogate dual objective functions are given, regarded as functions of three variables (namely, of the primal constraint set, the primal objective function and the dual variable).Abstract:
For constrained primal infimization problems, we give some characterizations of the surrogate dual objective functions, regarded as functions of three variables (namely, of the primal constraint set, the primal objective function and the dual variable). We also give some results on surrogate constraint mappingsread more
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Downward Sets and their separation and approximation properties
TL;DR: A theory of downward subsets of the space ℝI, where I is a finite index set, and two kinds of duality for downward sets, based on multiplicative and additive min-type functions, respectively, and corresponding separation properties are discussed.
Journal ArticleDOI
V -dualities and ⊥-dualities
TL;DR: In this article, the authors introduce and study dualities (i.e., mappings f e [Rbar]x → f △ e [rbar]w such that for all {fi }ie1 ∈ Rx and all index sets I), which satisfy the additional condition and their duals, which are characterized as those dualities △*:Rx → Rw for which, where ⊥ and ⊺ are two new binary operations on [RBar], which they introduce here.
Journal ArticleDOI
Duality in quasi-convex supremization and reverse convex infimization via abstract convex analysis,and applications to approximation **
TL;DR: In this paper, duality theorems and dual characterizations of optimal solutions for quasi-convex supremization and inverse convex infimization problems with abstract reverse convex constraint sets are given.
Journal ArticleDOI
Dual representations of hulls for functions satisfying f (0) = inf f (X\{0}) *
TL;DR: In this paper, a general theory of dual representations, without any extra parameters, of various hulls for extended-real valued functions on X satisfying f(0)= inf f(X\{0}) was given.
Journal ArticleDOI
Some characterizations of perturbational dual problems
TL;DR: In this article, the perturbational dual objective functions and the associated Lagrangians are characterized as functions of their natural variables and of the primal parameters, and some characterizations of various classes of perturbations and their associated marginal functions are given.
References
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Journal ArticleDOI
Dualities between complete lattices
TL;DR: In this article, the authors studied dualities between two complete lattices E and Fi and gave characterizations and representations of dualities, and some results on the dual △* F→Eof △ and on the associated hull operator △ *△:E→Ein the general case and in various particular eases.
Journal ArticleDOI
A general theory of dual optimization problems
TL;DR: In this article, a unified theory of dual optimization problems is presented, which encompasses the known dual problems, as well as particular cases of existing dual problems such as perturbation functions.
Journal ArticleDOI
V -dualities and ⊥-dualities
TL;DR: In this article, the authors introduce and study dualities (i.e., mappings f e [Rbar]x → f △ e [rbar]w such that for all {fi }ie1 ∈ Rx and all index sets I), which satisfy the additional condition and their duals, which are characterized as those dualities △*:Rx → Rw for which, where ⊥ and ⊺ are two new binary operations on [RBar], which they introduce here.
Journal ArticleDOI
Infimal generators and dualities between complete lattices
TL;DR: In this article, Kutateladze and Rubinov give some applications of infimal generators of complete lattices to the study of dualities between two complete lattice E and F.
Journal ArticleDOI
A general theory of surrogate dual and perturbational extended surrogate dual optimization problems
TL;DR: In this paper, the authors introduce and study two general concepts of dual problems, encompassing the classical surrogate dual problem, and show some relations between these problems and the dual problems to (P ) defined with the aid of a perturbation and a concept of conjugation of functionals.