84 citations · 155 across the 13 of their papers we have counts for
14 papers
Set Relations and Approximate Solutions in Set Optimization
Giovanni Crespi, Andreas H Hamel, Matteo Rocca +1
Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets.…
Remarks on Lagrange Multiplier Rules in Set Valued Optimization
Carola Schrage
In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which p…
Weak Minimizers, Minimizers and Variational Inequalities for set valued Functions. A blooming wreath?
Giovanni P. Crespi, Carola Schrage
In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in…
Variational inequalities characterizing weak minimality in set optimization
Giovanni P. Crespi, MatteoRocca, Carola Schrage
We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, re…
Set optimization - a rather short introduction
Andreas H. Hamel, Frank Heyde, Andreas Löhne +2
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-valu…
A Minty variational principle for set optimization
Giovanni P. Crespi, Andreas H. Hamel, Carola Schrage
Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradig…
Applying Set Optimization to Weak Efficiency
Giovanni P. Crespi, Carola Schrage
Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variationa…
Set-optimization meets variational inequalities
Giovanni P. Crespi, Carola Schrage
We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a s…
An Algorithm to Solve Polyhedral Convex Set Optimization Problems
Andreas Löhne, Carola Schrage
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solu…
Directional derivatives and subdifferentials of set-valued convex functions
Andreas H. Hamel, Carola Schrage
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new c…
Continuity of Convex Set-valued Maps and a Fundamental Duality Formula for Set-valued Optimization
Frank Heyde, Carola Schrage
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For…
Conjugate Duality of Set--Valued Functions
Carola Schrage
To a function with values in the power set of a pre--ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original functio…
Notes about extended real- and set-valued functions
Andreas H. Hamel, Carola Schrage
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving and/or…
Scalar Representation and Conjugation of Set-Valued Functions
Carola Schrage
To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function…