[图书][B] Set-valued optimization
AA Khan, C Tammer, C Zalinescu - 2016 - Springer
Set-valued optimization is a vibrant and expanding branch of applied mathematics that
deals with optimization problems where the objective map and/or the constraint maps are …
deals with optimization problems where the objective map and/or the constraint maps are …
[图书][B] Vector optimization
J Jahn - 2009 - Springer
The continuous and increasing interest concerning vector optimization perceptible in the
research community, where contributions dealing with the theory of duality abound lately …
research community, where contributions dealing with the theory of duality abound lately …
[图书][B] Vector optimization with infimum and supremum
A Löhne - 2011 - books.google.com
The theory of Vector Optimization is developed by a systematic usage of infimum and
supremum. In order to get existence and appropriate properties of the infimum, the image …
supremum. In order to get existence and appropriate properties of the infimum, the image …
Set optimization—a rather short introduction
Recent developments in set optimization are surveyed and extended including various set
relations as well as fundamental constructions of a convex analysis for set-and vector …
relations as well as fundamental constructions of a convex analysis for set-and vector …
A duality theory for set-valued functions I: Fenchel conjugation theory
AH Hamel - Set-Valued and Variational Analysis, 2009 - Springer
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 set-valued …
preordered, separated locally convex space is the pointwise supremum of its set-valued …
A new approach to duality in vector optimization
A Löhne, C Tammer - Optimization, 2007 - Taylor & Francis
In this article, we develop a new approach to duality theory for convex vector optimization
problems. We modify a given (set-valued) vector optimization problem such that the image …
problems. We modify a given (set-valued) vector optimization problem such that the image …
Lagrange duality in set optimization
Based on the complete-lattice approach, a new Lagrangian type duality theory for set-valued
optimization problems is presented. In contrast to previous approaches, set-valued versions …
optimization problems is presented. In contrast to previous approaches, set-valued versions …
Optimization with set relations: conjugate duality
A Löhne* - Optimization, 2005 - Taylor & Francis
The aim of this article is to develop a conjugate duality theory, based on set relation
approach, for convex set-valued maps. The basic idea is to understand a convex set-valued …
approach, for convex set-valued maps. The basic idea is to understand a convex set-valued …
A Fenchel–Rockafellar duality theorem for set-valued optimization
AH Hamel - Optimization, 2011 - Taylor & Francis
A duality theorem of the Fenchel–Rockafellar type for set-valued optimization problems is
presented along with a result for the conjugate of the sum of two set-valued functions and a …
presented along with a result for the conjugate of the sum of two set-valued functions and a …
A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa's set approach
TXD Ha - Mathematical Methods of Operations Research, 2020 - Springer
In this paper, we introduce a new concept of slope for a set-valued map using a scalarizing
function defined with the help of the Hiriart-Urruty signed distance function. It turns out that …
function defined with the help of the Hiriart-Urruty signed distance function. It turns out that …