Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Schrage, Carola"'
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. A function mappping into the preordered set is extended to a complete
Externí odkaz:
http://arxiv.org/abs/1812.03300
Autor:
Schrage, Carola
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 proves that under rather mild assumptions, $x$ is a weak solution to th
Externí odkaz:
http://arxiv.org/abs/1612.00255
Autor:
Crespi, Giovanni P., Schrage, Carola
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 a conlinear space. Similar results are proved for a weaker concept of
Externí odkaz:
http://arxiv.org/abs/1409.3383
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, respectively, are proved. As an application, we obtain necessary and suf
Externí odkaz:
http://arxiv.org/abs/1407.4292
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-valued functions, and duality for set optimization problems. Extensive sec
Externí odkaz:
http://arxiv.org/abs/1404.5928
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 paradigm in vector optimization, the solution concept for such problems, intr
Externí odkaz:
http://arxiv.org/abs/1403.2898
Autor:
Crespi, Giovanni P., Schrage, Carola
Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend those known
Externí odkaz:
http://arxiv.org/abs/1403.2860
Autor:
Crespi, Giovanni P., Schrage, Carola
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 solution we deal with has been introduced Heyde and Loehne, for convex
Externí odkaz:
http://arxiv.org/abs/1303.4212
Autor:
Löhne, Andreas, Schrage, Carola
Publikováno v:
Optimization, 62, No. 1, 131-141, 2013
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 solution is understood to be a set of points in the domain satisfying two
Externí odkaz:
http://arxiv.org/abs/1210.0729
Autor:
Hamel, Andreas H., Schrage, Carola
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 concepts are used to characterize solutions of convex optimization prob
Externí odkaz:
http://arxiv.org/abs/1207.5295