@misc{Steinbach, author = {Steinbach, Marc}, title = {Autos, Ziegen und Streith{\"a}hne}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6087}, number = {00-40}, abstract = {Das aus den Medien bekannte umstrittene Ziegenproblem (auch Drei-T{\"u}ren-Problem genannt) wird vollst{\"a}ndig analysiert und gel{\"o}st. In der Streitfrage spielen sprachliche Mehrdeutigkeiten der Problemformulierung eine wesentliche Rolle; zudem werden Zufallsereignisse mit willk{\"u}rlicher Information {\"u}ber deren Ergebnisse verwechselt. Tats{\"a}chlich erweisen sich beide strittigen L{\"o}sungen als teilweise richtige Bestandteile der Gesamtl{\"o}sung. Die Argumentation wird in allgemeinverst{\"a}ndlicher Sprache gef{\"u}hrt und anschliessend durch eine formale mathematische Betrachtung erg{\"a}nzt.}, language = {de} } @misc{Steinbach, author = {Steinbach, Marc}, title = {Hierarchical Sparsity in Multistage Convex Stochastic Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5837}, number = {00-15}, abstract = {Interior point methods for multistage stochastic programs involve KKT systems with a characteristic global block structure induced by dynamic equations on the scenario tree. We generalize the recursive solution algorithm proposed in an earlier paper so that its linear complexity extends to a refined tree-sparse KKT structure. Then we analyze how the block operations can be specialized to take advantage of problem-specific sparse substructures. Savings of memory and operations for a financial engineering application are discussed in detail.}, language = {en} } @misc{HenrionLiMoelleretal., author = {Henrion, Rene and Li, Pu and M{\"o}ller, Andris and Steinbach, Marc and Wendt, Moritz and Wozny, G{\"u}nter}, title = {Stochastic Optimization for Operating Chemical Processes Under Uncertainty}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6304}, number = {01-04}, abstract = {Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization.}, language = {en} } @misc{FuegenschuhGeisslerGollmeretal., author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Rene and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets}, issn = {1438-0064}, doi = {10.1007/s12667-013-0099-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17821}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.}, language = {en} } @article{FuegenschuhGeisslerGollmeretal., author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Ren{\´e} and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets}, series = {Energy Systems}, volume = {5}, journal = {Energy Systems}, number = {3}, publisher = {Springer Berlin Heidelberg}, address = {Berlin}, doi = {10.1007/s12667-013-0099-8}, pages = {449 -- 473}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network's capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations.}, language = {en} }