Spreading activation: a fast calculation method for text centroids. - In: Theory and application of text-representing centroids, (2019), S. 27-38
On a class of non-Hermitian matrices with positive definite Schur complements. - In: Proceedings of the American Mathematical Society, ISSN 1088-6826, Bd. 147 (2019), 6, S. 2375-2388
https://doi.org/10.1090/proc/14412
Solving multiobjective mixed integer convex optimization problems. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (26 Seiten). - (Preprint ; M19,06)
Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, but we built linear outer approximations of the image set in an adaptive way. We are able to guarantee correctness in terms of detecting both the efficient and the nondominated set of multiobjective mixed integer convex problems according to a prescribed precision. As far as we know, the procedure we present is the first deterministic algorithm devised to handle this class of problems. Our numerical experiments show results on biobjective and triobjective mixed integer convex instances.
https://www.db-thueringen.de/receive/dbt_mods_00038620
Numerical results for the multiobjective trust region algorithm MHT. - In: Data in Brief, ISSN 2352-3409, Bd. 25 (2019), 104103, S. 1-18
https://doi.org/10.1016/j.dib.2019.104103
The non-real spectrum of a singular indefinite Sturm-Liouville operator with regular left endpoint. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (3 Seiten). - (Preprint ; M19,05)
https://www.db-thueringen.de/receive/dbt_mods_00038524
A branch-and-bound-based algorithm for nonconvex multiobjective optimization. - In: SIAM journal on optimization, ISSN 1095-7189, Bd. 29 (2019), 1, S. 794-821
https://doi.org/10.1137/18M1169680
Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials. - In: Journal of differential equations, ISSN 1090-2732, Bd. 267 (2019), 1, S. 468-493
https://doi.org/10.1016/j.jde.2019.01.013
An algorithm for computing Fréchet means on the sphere. - In: Optimization letters, ISSN 1862-4480, Bd. 13 (2019), 7, S. 1523-1533
For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special global problem over the sphere, namely the determination of Fréchet means, which are points minimising the mean distance to a given set of points. The Branch and Bound method derived needs no further assumptions on the input data, but is able to cope with this objective function which is neither convex nor differentiable. The algorithms performance is tested on simulated and real data.
https://doi.org/10.1007/s11590-019-01415-y
Spectral enclosures for a class of block operator matrices. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (23 Seiten). - (Preprint ; M19,04)
We prove new spectral enclosures for the non-real spectrum of a class of 2x2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200198
Optimal control of differential-algebraic equations from an ordinary differential equation perspective. - In: Optimal control, applications and methods, ISSN 1099-1514, Bd. 40 (2019), 2, S. 351-366
https://doi.org/10.1002/oca.2481