Nichtlineare Optimierung

Reinhardt, Rüdiger; Hoffmann, Armin; Gerlach, Tobias

doi:10.1007/978-3-8274-2949-0

Cited by 11 publications

(5 citation statements)

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“…(2.8) Assuming (2.8) to be a continuous and convex function, ρ * can be determined using numerical optimization strategies such as gradient descent [HS06;RHG13] or the Nelder-Mead method, also called downhill simplex method [NM65;Pow62]. These try to estimate a function's global minimum (or maximum) using multiple iterations, like known from Newton's method [New67].…”

Section: Chapter 2 Probabilistic Sensor Modelsmentioning

confidence: 99%

Smartphone-Based 3D Indoor Localization and Navigation

Ebner¹

2021

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During my master's thesis, which covered the essentials of Wi-Fi location estimation, I came in contact with the concepts of indoor localization, and multi sensor fusion. Having attracted my interest, I hereafter joined the Faculty of Computer Science and Business Information Systems at the University of Applied Sciences Würzburg-Schweinfurt as a research assistant. During that time I conducted the majority of my research on indoor localization and navigation, which finally lead to writing this work.I would like to thank my colleagues during that time, but especially my local doctoral adviser Prof. Dr. Frank Deinzer. Not only did he guide me towards earning a doctors degree, he also provided extensive feedback to all publications, always ensuring utmost scientific quality. I would also like to thank my external doctoral adviser and first referee Prof. Dr. habil. Marcin Grzegorzek for his trust, all provided feedback, and the warm welcome within his research group. I also owe gratitude to my co-workers Lukas, Toni, and Markus. Without hours of mutual feedback, technical input, paired programming, data acquisition, and networking, this work would not have been possible. Likewise, I also wish to thank Prof. Dr. Karsten Huffstadt and Prof. Dr. Arndt Balzer for helping with funding my initial employment.In order to develop a generic indoor localization and navigation solution, the presented system was deployed to and tested within several unique buildings. For this, special thanks go to Dr. Hellmuth Möhring from the RothenburgMuseum in Rothenburg ob der Tauber, Prof. Dr. Günther Moosbauer from the Gäubodenmuseum in Straubing, Angelika Schreiber from the Hutmuseum in Lindenberg, the Landesstelle für die nichtstaatlichen Museen in Bayern, and the Sparkassenstiftung. By providing access and enabling temporal hardware installations they allowed gathering data within a range of unique and representative public buildings, enhancing the quality of the developed system, and the experiments provided within this work.Thanks also go to Markus, Christin, Alexander, and Maximilian, not only for spending numerous hours of their spare time with proof reading and feedback, but also for all emotional support while conducting my research and writing this work. The same goes to my parents, for always supporting me, and my education.To Katharina, who has been a true friend, and will never be forgotten.

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Section: Chapter 2 Probabilistic Sensor Modelsmentioning

confidence: 99%

Smartphone-Based 3D Indoor Localization and Navigation

Ebner¹

2021

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“…In an abstract sense, the Frobenius norm of a matrix A ∈ R n×m + is equal to the Euclidean distance of a vector a ∈ R n•m + . To be more precise the Frobenius norm is the square root of the sum of all squared matrix elements (Reinhardt et al, 2013):…”

Section: Error Functionmentioning

confidence: 99%

“…Besides this general definition there do exist alternative representations, among others the representation using the trace of a matrix (Reinhardt et al, 2013):…”

Section: Error Functionmentioning

confidence: 99%

nmfgpu4R: GPU-Accelerated Computation of the Non-Negative Matrix Factorization (NMF) Using CUDA Capable Hardware

Koitka¹,

Friedrich²

2016

The R Journal

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In this work, a novel package called nmfgpu4R is presented, which offers the computation of Non-negative Matrix Factorization (NMF) on Compute Unified Device Architecture (CUDA) platforms within the R environment. Benchmarks show a remarkable speed-up in terms of time per iteration by utilizing the parallelization capabilities of modern graphics cards. Therefore the application of NMF gets more attractive for real-world sized problems because the time to compute a factorization is reduced by an order of magnitude.

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“…The optimisation problem which needs to be solved for each agent is a quadratic optimisation problem with complementarity constraints. The objective function and the constraints (4) and 5 with a penalty factor r. This optimisation problem has the same optimum as the original optimisation problem for r → ∞ [23]. In [22] [24] [25] it was shown that the above approach converges despite of the complementarity constraints which violate the linear independence constraint qualification.…”

Section: Bargaining Algorithmmentioning

confidence: 99%

“…There are various ways to solve such kind of problems, e.g. interior point method, augmented Lagrangian methods, or conditional gradient method [23] [26] [27]. In this paper, the conditional gradient method [28] is used, because it can be easily obtained by extending the simplex algorithm, see e.g.…”

Section: Bargaining Algorithmmentioning

confidence: 99%

Multi-Energy Simulation of a Smart Grid with Optimal Local Demand and Supply Management

Kuschel¹,

Köstler²,

Rüde³

2015

SGRE

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A simulation approach of a smart grid by cooperative bargaining is presented in this paper. Each participant of the smart grid determines its optimal schedule to meet its power and heating demand at minimal costs employing solar panels, fuel cells and batteries. This is done by solving a quadratic optimisation problem which takes the energy prices and the available devices into account. The energy prices are related to the demand and supply in the smart grid, so that a lower demand yields lower prices. The cooperative bargaining game is used to tune the participants' optimal solution to obtain a Nash equilibrium. The computed solutions of the participants are validated against the capacities and structure of the smart grid by solving a multi-commodity flow problem. The presented model features multiple types of energy, so that they may be substituted to meet the participants' demand. Furthermore, the participants may also act as supplier and not only as consumer, which allows decentralised generation of energy. The approach is validated in several experiments where effects like negative energy prices if generated energy exceeds the smart grid's total demand and peak-shaving with even small-capacity batteries are exhibited.

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Nichtlineare Optimierung

Cited by 11 publications

References 0 publications

Smartphone-Based 3D Indoor Localization and Navigation

Smartphone-Based 3D Indoor Localization and Navigation

nmfgpu4R: GPU-Accelerated Computation of the Non-Negative Matrix Factorization (NMF) Using CUDA Capable Hardware

Multi-Energy Simulation of a Smart Grid with Optimal Local Demand and Supply Management

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