@misc{BurgschweigerGnaedigSteinbach2005, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8657}, number = {05-31}, year = {2005}, abstract = {Mathematical decision support for operative planning in water supply systems is highly desirable but leads to very difficult optimization problems. We propose a nonlinear programming approach that yields practically satisfactory operating schedules in acceptable computing time even for large networks. Based on a carefully designed model supporting gradient-based optimization algorithms, this approach employs a special initialization strategy for convergence acceleration, special minimum up and down time constraints together with pump aggregation to handle switching decisions, and several network reduction techniques for further speed-up. Results for selected application scenarios at Berliner Wasserbetriebe demonstrate the success of the approach.}, language = {en} } @misc{BurgschweigerGnaedigSteinbach2005, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Optimierte Tagesplanung im Berliner Trinkwassernetz}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8668}, number = {05-32}, year = {2005}, abstract = {Der Artikel beschreibt ein mathematisches Optimierungssystem zur Betriebsplanung in großen Wassernetzen, das bei den Berliner Wasserbetrieben eingesetzt wird. F{\"u}r das Berliner Versorgungsnetz werden Optimierungsergebnisse vorgestellt.}, language = {de} } @misc{Steinbach2004, 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}, year = {2004}, 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{BurgschweigerGnaedigSteinbach2004, author = {Burgschweiger, Jens and Gn{\"a}dig, Bernd and Steinbach, Marc}, title = {Optimization Models for Operative Planning in Drinking Water Networks}, doi = {10.1007/s11081-008-9040-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8237}, number = {04-48}, year = {2004}, abstract = {The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.}, language = {en} } @misc{BertholdGleixner2012, author = {Berthold, Timo and Gleixner, Ambros}, title = {Undercover: a primal MINLP heuristic exploring a largest sub-MIP}, issn = {1438-0064}, doi = {10.1007/s10107-013-0635-2}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14631}, number = {12-07}, year = {2012}, abstract = {We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers.}, language = {en} } @misc{BertholdGleixner2009, author = {Berthold, Timo and Gleixner, Ambros}, title = {Undercover - a primal heuristic for MINLP based on sub-MIPs generated by set covering}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11632}, number = {09-40}, year = {2009}, abstract = {We present Undercover, a primal heuristic for mixed-integer nonlinear programming (MINLP). The heuristic constructs a mixed-integer linear subproblem (sub-MIP) of a given MINLP by fixing a subset of the variables. We solve a set covering problem to identify a minimal set of variables which need to be fixed in order to linearise each constraint. Subsequently, these variables are fixed to approximate values, e.g. obtained from a linear outer approximation. The resulting sub-MIP is solved by a mixed-integer linear programming solver. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. Although general in nature, the heuristic seems most promising for mixed-integer quadratically constrained programmes (MIQCPs). We present computational results on a general test set of MIQCPs selected from the MINLPLib.}, language = {en} } @misc{BertholdGleixnerHeinzetal.2013, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {Analyzing the computational impact of MIQCP solver components}, issn = {1438-0064}, doi = {10.3934/naco.2012.2.739}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17754}, year = {2013}, abstract = {We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.}, language = {en} } @misc{BertholdGleixnerHeinzetal.2011, author = {Berthold, Timo and Gleixner, Ambros and Heinz, Stefan and Vigerske, Stefan}, title = {On the computational impact of MIQCP solver components}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11998}, number = {11-01}, year = {2011}, abstract = {We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on linear outer approximation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.}, language = {en} } @misc{BestuzhevaGleixnerVoelker2022, author = {Bestuzheva, Ksenia and Gleixner, Ambros and V{\"o}lker, Helena}, title = {Strengthening SONC Relaxations with Constraints Derived from Variable Bounds}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88306}, year = {2022}, abstract = {Certificates of polynomial nonnegativity can be used to obtain tight dual bounds for polynomial optimization problems. We consider Sums of Nonnegative Circuit (SONC) polynomials certificates, which are well suited for sparse problems since the computational cost depends only on the number of terms in the polynomials and does not depend on the degrees of the polynomials. This work is a first step to integrating SONC-based relaxations of polynomial problems into a branch-and-bound algorithm. To this end, the SONC relaxation for constrained optimization problems is extended in order to better utilize variable bounds, since this property is key for the success of a relaxation in the context of branch-and-bound. Computational experiments show that the proposed extension is crucial for making the SONC relaxations applicable to most constrained polynomial optimization problems and for integrating the two approaches.}, language = {en} } @misc{VuLitzelKoch2025, author = {Vu, Thi Huong and Litzel, Ida and Koch, Thorsten}, title = {Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives}, arxiv = {http://arxiv.org/abs/2506.04045}, year = {2025}, abstract = {Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -- containing about 70 million articles and a billion citations -- poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem's structure. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data.}, language = {en} }