Set approach for set optimization with variable ordering structures. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 37 S., 434,7 KB). - (Preprint ; M14,11)
This paper aims at combining variable ordering structures with set relations in set optimization, which have been dened using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the relations from [16, 25] and discuss their usefulness. After analyzing the properties of the introduced relations, we dene new solution notions for set-valued optimization problems equipped with variable ordering structures and compare them with other concepts from the literature. In order to characterize the introduced solutions a nonlinear scalarization approach is used.
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A discretization of Boltzmann's collision operator with provable convergence. - In: AIP conference proceedings, ISSN 1551-7616, Bd. 1628 (2014), S. 1024-1031
http://dx.doi.org/10.1063/1.4902706
Translation invariant kinetic models on integer lattices. - In: AIP conference proceedings, ISSN 1551-7616, Bd. 1628 (2014), S. 640-647
http://dx.doi.org/10.1063/1.4902653
The Mondshein sequence. - In: Automata, Languages, and Programming, (2014), S. 967-978
http://dx.doi.org/10.1007/978-3-662-43948-7_80
Properly optimal elements in vector optimization with variable ordering structures. - In: Journal of global optimization, ISSN 1573-2916, Bd. 60 (2014), 4, S. 689-712
https://doi.org/10.1007/s10898-013-0132-4
A growth condition for Hamiltonian systems related with Krein strings. - In: Acta scientiarum mathematicarum, ISSN 2064-8316, Bd. 80 (2014), 1/2, S. 31-94
http://dx.doi.org/10.14232/actasm-012-028-8
The invertibility of 2 x 2 operator matrices. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 19 S., 305 KB). - (Preprint ; M14,10)
In this paper the properties of right invertible row operators, i.e., of 1x2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2x2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.
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Variational principles for self-adjoint operator functions arising from second-order systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 30 S., 455 KB). - (Preprint ; M14,09)
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Multi-objective optimization in the Lorentz force velocimetry framework. - In: Book of digests & program, (2014), S. 81-82
Ekeland's variational principle for vector optimization with variable ordering structure. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 24 S., 351 KB). - (Preprint ; M14,08)
There are many generalizations of Ekeland's variational principle for vector optimization problems with fixed ordering structures, i.e., ordering cones. These variational principles are useful for deriving optimality conditions, epsilon-Kolmogorov conditions in approximation theory, and epsilon-maximum principles in optimal control. Here, we present several generalizations of Ekeland's variational principle for vector optimization problems with respect to variable ordering structures. For deriving these variational principles we use nonlinear scalarization techniques. Furthermore, we derive necessary conditions for approximate solutions of vector optimization problems with respect to variable ordering structures using these variational principles and the subdifferential calculus by Mordukhovich.
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