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Prof. Dr. rer. nat. habil. Matthias Kriesell


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Veröffentlichungen am Institut für Mathematik seit 1990

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Kostochka, Alexandr V.; Stiebitz, Michael;
The minimum number of edges in 4-critical digraphs of given order. - In: Graphs and combinatorics. - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 36 (2020), 3, S. 703-718
Lo, On-Hei Solomon; Schmidt, Jens M.; Van Cleemput, Nico; Zamfirescu, Carol T.;
Shortness coefficient of cyclically 4-edge-connected cubic graphs. - In: The electronic journal of combinatorics. - [Madralin] : EMIS ELibEMS, ISSN 10778926, Volume 27 (2020), issue 1, P1.43, Seite 1-14
Mehrez, Mohamed W.; Worthmann, Karl; Cenerini, Joseph P. V.; Osman, Mostafa; Melek, William W.; Jeon, Soo;
Model predictive control without terminal constraints or costs for holonomic mobile robots. - In: Robotics and autonomous systems : international journal.. - Amsterdam [u.a.] : Elsevier, ISSN 1872-793X, Bd. 127 (2020), 103468
Giribet, Juan; Langer, Matthias; Martínez Pería, Francisco; Philipp, Friedrich; Trunk, Carsten;
Spectral enclosures for a class of block operator matrices. - In: Journal of functional analysis. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0783, Bd. 278 (2020), 10, S. 108455
Hildenbrandt, Regina;
The k-server problem with parallel requests and the compound work function algorithm. - In: Baltic journal of modern computing : BJMC.. - [S.l.], ISSN 2255-8950, Bd. 8 (2020), 1, S. 1-20

In this paper the compound work function algorithm for solving the generalized k-server problem is proposed. This problem is an online k-server problem with parallel requests where several servers can also be located on one point. In 1995 Koutsoupias and Papadimitriouhave proved that the well-known work function algorithm is competitive for the (usual) k-server problem. A proof, where a potential-like function argument is included, was given by Borodinand El-Yaniv in 1998. Unfortunately, certain techniques of these proofs cannot be applied to show that a natural generalization of the work function algorithm is competitive for the problem with parallel requests. Values of work functions, which are used by the compound work function algorithm are derived from a surrogate problem, where at most one server must be moved in servicing the request in each step. We can show that the compound work function algorithm is competitive with the same bound of the ratio as in the case of the usual problem.
Kriesell, Matthias;
Maximal ambiguously k-colorable graphs. - In: Journal of combinatorial theory : JCTB.. - Orlando, Fla. : Academic Press, Bd. 140 (2020), S. 248-262
Rocktäschel, Stefan;
A branch-and-bound algorithm for multiobjective mixed-integer convex optimization. - Wiesbaden : Springer Spektrum, 2020. - VIII, 70 Seiten. . - (BestMasters) ISBN 978-3-658-29148-8

Sauerteig, Philipp; Worthmann, Karl;
Towards multiobjective optimization and control of smart grids. - In: Optimal control, applications and methods. - New York, NY [u.a.] : Wiley, ISSN 1099-1514, Bd. 41 (2020), 1, S. 128-145
Preißer, Johanna E.; Schmidt, Jens M.;
Computing vertex-disjoint paths in large graphs using MAOs. - In: Algorithmica : an international journal in computer science.. - New York, NY : Springer, ISSN 1432-0541, Bd. 82 (2020), 1, S. 146-162
Eichfelder, Gabriele; Niebling, Julia; Rocktäschel, Stefan;
An algorithmic approach to multiobjective optimization with decision uncertainty. - In: Journal of global optimization : an international journal dealing with theoretical and computational aspects of seeking global optima and their applications in science, management and engineering.. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1573-2916, Bd. 77 (2020), 1, S. 3-25

In real life applications, optimization problems with more than one objective function are often of interest. Next to handling multiple objective functions, another challenge is to deal with uncertainties concerning the realization of the decision variables. One approach to handle these uncertainties is to consider the objectives as set-valued functions. Hence, the image of one decision variable is a whole set, which includes all possible outcomes of this decision variable. We choose a robust approach and thus these sets have to be compared using the so-called upper-type less order relation. We propose a numerical method to calculate a covering of the set of optimal solutions of such an uncertain multiobjective optimization problem. We use a branch-and-bound approach and lower and upper bound sets for being able to compare the arising sets. The calculation of these lower and upper bound sets uses techniques known from global optimization, as convex underestimators, as well as techniques used in convex multiobjective optimization as outer approximation techniques. We also give first numerical results for this algorithm.