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Decision Making with Dominance Constraints in Two-Stage Stochastic Integer Programming
Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables. He illustrates the superiority of the proposed decomposition method over standard solvers for example with numerical experiments with instances from energy investment.
Stochastic Optimization Methods in Finance and Energy
This volume presents a collection of contributions dedicated to applied problems in the financial and energy sectors that have been formulated and solved in a stochastic optimization framework. The invited authors represent a group of scientists and practitioners, who cooperated in recent years to facilitate the growing penetration of stochastic programming techniques in real-world applications, inducing a significant advance over a large spectrum of complex decision problems. After the recent widespread liberalization of the energy sector in Europe and the unprecedented growth of energy prices in international commodity markets, we have witnessed a significant convergence of strategic decis...
Evaluating Gas Network Capacities
"This book deals with a simple sounding question whether a certain amount of gas can be transported by a given pipeline network. While well studied for a single pipeline, this question gets extremely difficult if we consider a meshed nation wide gas transportation network, taking into account all the technical details and discrete decisions, as well as regulations, contracts, and varying demand. This book describes several mathematical models to answer these questions, discusses their merits and disadvantages, explains the necessary technical and regulatory background, and shows how to solve this question using sophisticated mathematical optimization algorithms."--
Shape Optimization under Uncertainty from a Stochastic Programming Point of View
Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.
Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty
The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, Jonas Schweiger addresses applications, where nonconvexity in the model and uncertainty in the data pose principal difficulties. In the first part, he contributes strong relaxations for non-convex problems such as the non-convex quadratic programming and the Pooling Problem. In the second part, he contributes a robust model for gas transport network extension and a custom decomposition approach. All results are backed by extensive computational studies.
Studien- und Berufsplaner Mathematik
Mathematik ist eine Schlüsseltechnologie für Technik und Wirtschaft. Dies ist eine wichtige Botschaft bei der Vermittlung von Mathematik in Schule und Hochschule. Die Berufsmöglichkeiten für Mathematikerinnen und Mathematiker sind interessant und vielseitig. Dieser Studien- und Berufsplaner Mathematik ist das nützliche Nachschlagewerk mit vielen Informationen für Studium und spätere Berufswahl speziell für das Fach Mathematik und eignet sich als Orientierungshilfe und Leitfaden zugleich. Er informiert über Wert, Attraktivität und Chancen des Mathematikstudiums und enthält zahlreiche Interviews und Berichte von Mathematikern und Mathematikerinnen aus Hochschule und Praxis. Die aktualisierte und überarbeitete Neuauflage bietet zusätzliche Praktikerporträts aus den verschiedenen Branchen und Unternehmensbereichen sowie zwei Specials zu den Themen Finanzmathematik und Modellierung, Simulation, Optimierung.
Märkte für Träume
Wer jede Woche Lotto spielt, gewinnt statistisch etwa alle 2,7 Millionen Jahre. Trotzdem hoffen Millionen Menschen jede Woche auf ihr Glück und Lotterien und Glücksspiele in Deutschland erzielen gewaltige Umsätze. Mithilfe zahlreicher statistischer Analysen versucht Mark Lutter dieses Massenphänomen zu ergründen. Welche Motive und Hoffnungen stehen hinter dem Loskauf? Und wie lässt sich aus soziologischer Perspektive die große Nachfrage nach einem Gut erklären, das sehr wahrscheinlich zum finanziellen Verlust des Einsatzes führen wird? Sein Fazit: Lotto ist ein "Markt für Träume", denn noch immer verkörpert die Lotterie das Versprechen, großer Wohlstand sei für alle erreichbar.
