@misc{Steinbach, author = {Steinbach, Marc}, title = {On PDE Solution in Transient Optimization of Gas Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8215}, number = {04-46}, abstract = {Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions---or as relaxation in a branch and bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse local projections, based on the KKT systems' structual properties induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a control space method and with the multifrontal solver MA27 are provided.}, language = {en} } @misc{EhrhardtSteinbach, author = {Ehrhardt, Klaus and Steinbach, Marc}, title = {KKT Systems in Operative Planning for Gas Distribution Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7962}, number = {04-21}, abstract = {Operative planning in gas networks with prescribed binary decisions yields large scale nonlinear programs defined on graphs. We study the structure of the KKT systems arising in interior methods and present a customized direct solution algorithm. Computational results indicate that the algorithm is suitable for optimization in small and medium-sized gas networks.}, language = {en} } @misc{EhrhardtSteinbach, author = {Ehrhardt, Klaus and Steinbach, Marc}, title = {Nonlinear Optimization in Gas Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7687}, number = {03-46}, abstract = {The operative planning problem in natural gas distribution networks is addressed. An optimization model focusing on the governing PDE and other nonlinear aspects is presented together with a suitable discretization for transient optimization in large networks by SQP methods. Computational results for a range of related dynamic test problems demonstrate the viability of the approach.}, language = {en} }