@misc{GamrathAndersonBestuzhevaetal.2020, author = {Gamrath, Gerald and Anderson, Daniel and Bestuzheva, Ksenia and Chen, Wei-Kun and Eifler, Leon and Gasse, Maxime and Gemander, Patrick and Gleixner, Ambros and Gottwald, Leona and Halbig, Katrin and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Le Bodic, Pierre and Maher, Stephen J. and Matter, Frederic and Miltenberger, Matthias and M{\"u}hmer, Erik and M{\"u}ller, Benjamin and Pfetsch, Marc and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Tawfik, Christine and Vigerske, Stefan and Wegscheider, Fabian and Weninger, Dieter and Witzig, Jakob}, title = {The SCIP Optimization Suite 7.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-78023}, year = {2020}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders' decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders' decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP.}, language = {en} } @misc{GleixnerEiflerGallyetal.2017, author = {Gleixner, Ambros and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gemander, Patrick and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Vigerske, Stefan and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 5.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66297}, year = {2017}, abstract = {This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 \% faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 \% faster overall and 23 \% faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG.}, language = {en} } @misc{HasenfelderLehmannRadonsetal.2018, author = {Hasenfelder, Richard and Lehmann, Lutz and Radons, Manuel and Streubel, Tom and Strohm, Christian and Griewank, Andreas}, title = {Computational aspects of the Generalized Trapezoidal Rule}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68615}, year = {2018}, abstract = {In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side F:IR^n -> IR^n. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a non-differentiability of F. In such a situation the investigated generalized trapezoidal rule achieves a higher convergence order than the classical method. While the asymptotic behavior of the generalized method was investigated in a previous work, in the present article we develop the algorithmic structure for efficient implementation strategies and estimate the actual computational cost of the latter. Moreover, energy preservation of the generalized trapezoidal rule is proved for Hamiltonian systems with piecewise linear right hand side.}, language = {en} } @misc{GleixnerBastubbeEifleretal.2018, author = {Gleixner, Ambros and Bastubbe, Michael and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and L{\"u}bbecke, Marco and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Schubert, Christoph and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Walter, Matthias and Wegscheider, Fabian and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 6.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69361}, year = {2018}, abstract = {The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders' decomposition in a generic framework. GCG's detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders' framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.}, language = {en} } @misc{GriewankHasenfelderRadonsetal.2017, author = {Griewank, Andreas and Hasenfelder, Richard and Radons, Manuel and Lehmann, Lutz and Streubel, Tom}, title = {Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1378653}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64639}, year = {2017}, abstract = {In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:R^n \to R^n\) based on a generalization of algorithmic differentiation. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a nondifferentiability of \(F\). The advantage of the proposed generalized trapezoidal rule is threefold: Firstly, we can achieve a higher convergence order than with the classical method. Moreover, the method is energy preserving for piecewise linear Hamiltonian systems. Finally, in analogy to the classical case we derive a third order interpolation polynomial for the numerical trajectory. In the smooth case the generalized rule reduces to the classical one. Hence, it is a proper extension of the classical theory. An error estimator is given and numerical results are presented.}, language = {en} } @misc{GriewankStreubelLehmannetal.2016, author = {Griewank, Andreas and Streubel, Tom and Lehmann, Lutz and Hasenfelder, Richard and Radons, Manuel}, title = {Piecewise linear secant approximation via Algorithmic Piecewise Differentiation}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1387256}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61642}, year = {2016}, abstract = {It is shown how piecewise differentiable functions \(F: R^n → R^m\) that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points x̌ and x̂. We show that the discrepancy between function and model at any point x is of the bilinear order O(||x - x̌|| ||x - x̂||). This is a little surprising since x ∈ R^n may vary over the whole Euclidean space, and we utilize only two function samples F̌ = F(x̌) and F̂ = F(x̂), as well as the intermediates computed during their evaluation. As an application of the piecewise linearization procedure we devise a generalized Newton's method based on successive piecewise linearization and prove for it sufficient conditions for convergence and convergence rates equaling those of semismooth Newton. We conclude with the derivation of formulas for the numerically stable implementation of the aforedeveloped piecewise linearization methods.}, language = {en} }