TY - GEN A1 - Steinbach, Marc T1 - On PDE Solution in Transient Optimization of Gas Networks N2 - 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. T3 - ZIB-Report - 04-46 KW - Gas network KW - operative planning KW - PDE constrained optimization KW - KKT system factorization KW - sparse projection method Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8215 ER - TY - GEN A1 - Ehrhardt, Klaus A1 - Steinbach, Marc T1 - KKT Systems in Operative Planning for Gas Distribution Networks N2 - 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. T3 - ZIB-Report - 04-21 KW - KKT system KW - sparse factorization KW - large-scale nonlinear program KW - gas network KW - operative planning Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7962 ER -