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An Algorithm Based on Semidefinite Programming for Finding Minimax
Takustr. 7 Zuse Institute Berlin 14195 Berlin Germany BELMIRO P.M. DUARTE,GUILLAUME SAGNOL,WENG KEE WONG An algorithm based on Semidefinite Programming for finding minimax optimal designs ZIB Report 18-01 (December 2017) Zuse Institute Berlin Takustr. 7 14195 Berlin Germany Telephone: +49 30-84185-0 Telefax: +49 30-84185-125 E-mail: [email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 An algorithm based on Semidefinite Programming for finding minimax optimal designs Belmiro P.M. Duarte a,b, Guillaume Sagnolc, Weng Kee Wongd aPolytechnic Institute of Coimbra, ISEC, Department of Chemical and Biological Engineering, Portugal. bCIEPQPF, Department of Chemical Engineering, University of Coimbra, Portugal. cTechnische Universität Berlin, Institut für Mathematik, Germany. dDepartment of Biostatistics, Fielding School of Public Health, UCLA, U.S.A. Abstract An algorithm based on a delayed constraint generation method for solving semi- infinite programs for constructing minimax optimal designs for nonlinear models is proposed. The outer optimization level of the minimax optimization problem is solved using a semidefinite programming based approach that requires the de- sign space be discretized. A nonlinear programming solver is then used to solve the inner program to determine the combination of the parameters that yields the worst-case value of the design criterion. The proposed algorithm is applied to find minimax optimal designs for the logistic model, the flexible 4-parameter Hill homoscedastic model and the general nth order consecutive reaction model, and shows that it (i) produces designs that compare well with minimax D−optimal de- signs obtained from semi-infinite programming method in the literature; (ii) can be applied to semidefinite representable optimality criteria, that include the com- mon A−; E−; G−; I− and D-optimality criteria; (iii) can tackle design problems with arbitrary linear constraints on the weights; and (iv) is fast and relatively easy to use. -
Solving Mixed Integer Linear and Nonlinear Problems Using the SCIP Optimization Suite
Takustraße 7 Konrad-Zuse-Zentrum D-14195 Berlin-Dahlem fur¨ Informationstechnik Berlin Germany TIMO BERTHOLD GERALD GAMRATH AMBROS M. GLEIXNER STEFAN HEINZ THORSTEN KOCH YUJI SHINANO Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite Supported by the DFG Research Center MATHEON Mathematics for key technologies in Berlin. ZIB-Report 12-27 (July 2012) Herausgegeben vom Konrad-Zuse-Zentrum f¨urInformationstechnik Berlin Takustraße 7 D-14195 Berlin-Dahlem Telefon: 030-84185-0 Telefax: 030-84185-125 e-mail: [email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite∗ Timo Berthold Gerald Gamrath Ambros M. Gleixner Stefan Heinz Thorsten Koch Yuji Shinano Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany, fberthold,gamrath,gleixner,heinz,koch,[email protected] July 31, 2012 Abstract This paper introduces the SCIP Optimization Suite and discusses the ca- pabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming frame- work SCIP. We explain how these can be used in concert to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, give an overview of available interfaces, and outline plans for future development. ∗A Japanese translation of this paper will be published in the Proceedings of the 24th RAMP Symposium held at Tohoku University, Miyagi, Japan, 27{28 September 2012, see http://orsj.or. -
Linear Underestimators for Bivariate Functions with a Fixed Convexity Behavior
Takustraße 7 Konrad-Zuse-Zentrum D-14195 Berlin-Dahlem fur¨ Informationstechnik Berlin Germany MARTIN BALLERSTEINy AND DENNIS MICHAELSz AND STEFAN VIGERSKE Linear Underestimators for bivariate functions with a fixed convexity behavior This work is part of the Collaborative Research Centre “Integrated Chemical Processes in Liquid Multiphase Systems” (CRC/Transregio 63 “InPROMPT”) funded by the German Research Foundation (DFG). Main parts of this work has been finished while the second author was at the Institute for Operations Research at ETH Zurich and financially supported by DFG through CRC/Transregio 63. The first and second author thank the DFG for its financial support. Thethirdauthor was supported by the DFG Research Center MATHEON Mathematics for key technologies and the Research Campus MODAL Mathematical Optimization and Data Analysis Laboratories in Berlin. y Eidgenossische¨ Technische, Hochschule Zurich,¨ Institut fur¨ Operations Research, Ramistrasse¨ 101, 8092 Zurich (Switzerland) z Technische Universitat¨ Dortmund, Fakultat¨ fur¨ Mathematik, M/518, Vogelpothsweg 87, 44227 Dortmund (Germany) ZIB-Report 13-02 (revised) (February 2015) Herausgegeben vom Konrad-Zuse-Zentrum fur¨ Informationstechnik Berlin Takustraße 7 D-14195 Berlin-Dahlem Telefon: 030-84185-0 Telefax: 030-84185-125 e-mail: [email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 Technical Report Linear Underestimators for bivariate functions with a fixed convexity behavior∗ A documentation for the SCIP constraint handler cons bivariate Martin Ballersteiny Dennis Michaelsz Stefan Vigerskex February 23, 2015 y Eidgenossische¨ Technische Hochschule Zurich¨ Institut fur¨ Operations Research Ramistrasse¨ 101, 8092 Zurich (Switzerland) z Technische Universitat¨ Dortmund Fakultat¨ fur¨ Mathematik, M/518 Vogelpothsweg 87, 44227 Dortmund (Germany) x Zuse Institute Berlin Takustr. -
Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks Jens Burgschweiger1, Bernd Gnädig2 and Marc C
14 The Open Applied Mathematics Journal, 2009, 3, 14-28 Open Access Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks Jens Burgschweiger1, Bernd Gnädig2 and Marc C. Steinbach3,* 1Berliner Wasserbetriebe, Abt. NA-G/W, 10864 Berlin, Germany 2Düsseldorf, Germany 3Leibniz Universität Hannover, IfAM, Welfengarten 1, 30167 Hannover, Germany Abstract: Mathematical decision support for operative planning in water supply systems is highly desirable; it leads, however, 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. Keywords: Water supply, large-scale nonlinear programming, convergence acceleration, discrete decisions, network reduction. INTRODUCTION • experiments with various optimization models and methods [36, 37], Stringent requirements on cost effectiveness and environmental compatibility generate an increased demand • a first nonlinear programming (NLP) model for model-based decision support tools for designing and developed under GAMS [38], operating municipal water supply systems. This paper deals • numerical results for a substantially reduced with the minimum cost operation of drinking water network graph using (under GAMS) the SQP codes networks. Operative planning in water networks is difficult: CONOPT, SNOPT, and the augmented Lagrangian a sound mathematical model leads to nonlinear mixed- code MINOS. -
Different Preservation Levels: the Case of Scholarly Digital Editions
Oltmanns, E, et al. 2019. Different Preservation Levels: The Case of Scholarly Digital Editions. Data Science Journal, 18: 51, pp. 1–9. DOI: https://doi.org/10.5334/dsj-2019-051 RESEARCH PAPER Different Preservation Levels: The Case of Scholarly Digital Editions Elias Oltmanns, Tim Hasler, Wolfgang Peters-Kottig and Heinz-Günter Kuper Department Scientific Information, Konrad-Zuse-Zentrum für Informationstechnik Berlin, DE Corresponding author: Elias Oltmanns ([email protected]) Ensuring the long-term availability of research data forms an integral part of data management services. Where OAIS compliant digital preservation has been established in recent years, in almost all cases the services aim at the preservation of file-based objects. In the Digital Human- ities, research data is often represented in highly structured aggregations, such as Scholarly Digital Editions. Naturally, scholars would like their editions to remain functionally complete as long as possible. Besides standard components like webservers, the presentation typically relies on project specific code interacting with client software like webbrowsers. Especially the latter being subject to rapid change over time invariably makes such environments awkward to maintain once funding has ended. Pragmatic approaches have to be found in order to balance the curation effort and the maintainability of access to research data over time. A sketch of four potential service levels aiming at the long-term availability of research data in the humanities is outlined: (1) Continuous Maintenance, (2) Application Conservation, (3) Application Data Preservation, and (4) Bitstream Preservation. The first being too costly and the last hardly satisfactory in general, we suggest that the implementation of services by an infrastructure provider should concentrate on service levels 2 and 3. -
54 OP08 Abstracts
54 OP08 Abstracts CP1 Dept. of Mathematics Improving Ultimate Convergence of An Aug- [email protected] mented Lagrangian Method Optimization methods that employ the classical Powell- CP1 Hestenes-Rockafellar Augmented Lagrangian are useful A Second-Derivative SQP Method for Noncon- tools for solving Nonlinear Programming problems. Their vex Optimization Problems with Inequality Con- reputation decreased in the last ten years due to the com- straints parative success of Interior-Point Newtonian algorithms, which are asymptotically faster. In the present research We consider a second-derivative 1 sequential quadratic a combination of both approaches is evaluated. The idea programming trust-region method for large-scale nonlin- is to produce a competitive method, being more robust ear non-convex optimization problems with inequality con- and efficient than its ”pure” counterparts for critical prob- straints. Trial steps are composed of two components; a lems. Moreover, an additional hybrid algorithm is defined, Cauchy globalization step and an SQP correction step. A in which the Interior Point method is replaced by the New- single linear artificial constraint is incorporated that en- tonian resolution of a KKT system identified by the Aug- sures non-accent in the SQP correction step, thus ”guiding” mented Lagrangian algorithm. the algorithm through areas of indefiniteness. A salient feature of our approach is feasibility of all subproblems. Ernesto G. Birgin IME-USP Daniel Robinson Department of Computer Science Oxford University [email protected] -
Using SCIP to Solve Your Favorite Integer Optimization Problem
Using SCIP to Solve Your Favorite Integer Optimization Problem Gregor Hendel, [email protected], www.zib.de/hendel Monash University, Melbourne March 12, 2019 Gregor Hendel{ Using SCIP 1/78 Zuse Institute Berlin { Fast Algorithms, Fast Computers A research institute and computing center of the State of Berlin with research units: • Numerical Analysis and Modeling • Visualization and Data Analysis • Optimization: Energy { Transportation { Health { Mathematical Optimization Methods • Scientific Information Systems • Computer Science and High Performance Computing Gregor Hendel{ Using SCIP 2/78 What is SCIP? SCIP (Solving Constraint Integer Programs) . • provides a full-scale MIP and MINLP solver, • is constraint based, • incorporates • MIP features (cutting planes, LP relaxation), and • MINLP features (spatial branch-and-bound, OBBT) • CP features (domain propagation), • SAT-solving features (conflict analysis, restarts), • is a branch-cut-and-price framework, • has a modular structure via plugins, • is free for academic purposes, • and is available in source-code under http://scip.zib.de ! Gregor Hendel{ Using SCIP 3/78 Meet the SCIP Team 31 active developers • 7 running Bachelor and Master projects • 16 running PhD projects • 8 postdocs and professors 4 development centers in Germany • ZIB: SCIP, SoPlex, UG, ZIMPL • TU Darmstadt: SCIP and SCIP-SDP • FAU Erlangen-N¨urnberg: SCIP • RWTH Aachen: GCG Many international contributors and users • more than 10 000 downloads per year from 100+ countries Careers • 10 awards for Masters and PhD theses: -
The SCIP Optimization Suite
The SCIP Optimization Suite Gerald Gamrath Zuse Institute Berlin EWO Seminar February 13, 2015 Gerald Gamrath (ZIB): The SCIP Optimization Suite 1 ZIB: Fast Algorithms – Fast Computers Konrad-Zuse-Zentrum für Informationstechnik Berlin I non-university research institute and computing center of the state of Berlin I Research Units: I numerical analysis and modeling I visualization and data analysis I optimization: energy–traffic–telecommunication–linear and nonlinear IP I scientific information systems I distributed algorithms and supercomputing I President: Martin Grötschel I more information: http://www.zib.de Gerald Gamrath (ZIB): The SCIP Optimization Suite 2 ZIB: Fast Algorithms – Fast Computers Konrad-Zuse-Zentrum für Informationstechnik Berlin I non-university research institute and computing center of the state of Berlin I Research Units: I numerical analysis and modeling I visualization and data analysis I optimization: energy–traffic–telecommunication–linear and nonlinear IP I scientific information systems I distributed algorithms and supercomputing I President: Martin Grötschel I more information: http://www.zib.de Gerald Gamrath (ZIB): The SCIP Optimization Suite 2 Outline SCIP –SolvingConstraintIntegerPrograms Constraint Integer Programming Solving Constraint Integer Programs History and Applications http://scip.zib.de Gerald Gamrath (ZIB): The SCIP Optimization Suite 3 What is a Constraint Integer Program? Mixed Integer Program Constraint Program Objective function: Objective function: . linear function . arbitrary function Feasible set: Feasible set: . described by linear constraints . given by arbitrary constraints Variable domains: Variable domains: . real or integer values . arbitrary (usually finite) min cT x min c(x) s.t. Ax ≤ b s.t. x ∈ F I C I (xI , xC ) ∈ Z × R (xI , xN ) ∈ Z × X Gerald Gamrath (ZIB): The SCIP Optimization Suite 4 What is a Constraint Integer Program? Constraint Integer Program Objective function: . -
Computational Aspects of Infeasibility Analysis in Mixed Integer Programming
Takustr. 7 Zuse Institute Berlin 14195 Berlin Germany JAKOB WITZIG TIMO BERTHOLD STEFAN HEINZ Computational Aspects of Infeasibility Analysis in Mixed Integer Programming ZIB Report 19-54 (November 2019) Zuse Institute Berlin Takustr. 7 14195 Berlin Germany Telephone: +49 30-84185-0 Telefax: +49 30-84185-125 E-mail: [email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 Computational Aspects of Infeasibility Analysis in Mixed Integer Programming Jakob Witzig,1 Timo Berthold,2 and Stefan Heinz3 1Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany [email protected] 2Fair Isaac Germany GmbH, Stubenwald-Allee 19, 64625 Bensheim, Germany [email protected] 3Gurobi GmbH, Ulmenstr. 37–39, 60325 Frankfurt am Main, Germany [email protected] November 6, 2019 Abstract The analysis of infeasible subproblems plays an important role in solv- ing mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to gener- ate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The result of this analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept is called conflict graph analysis and has its origin in solving satisfiability problems and is similarly used in con- straint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. Every ray of the dual LP provides a set of multipliers that can be used to generate a single new globally valid linear constraint. -
Classical Benders Decomposition (KC203) Cluster: CPAIOR Chair: Jean-François Cordeau, HEC Montreal
Sunday, May 29, 2016 9:00am - 10:00am Session: Classical Benders Decomposition (KC203) Cluster: CPAIOR Chair: Jean-François Cordeau, HEC Montreal Classical Benders Decomposition Jean-François Cordeau, HEC Montréal, [email protected] Benders decomposition is a mathematical decomposition technique designed to solve large- scale linear and mixed-integer programs comprising two sets of variables such that a more tractable subproblem is obtained when the values of some "complicating" variables are fixed. The technique works by projecting the original problem on the space of the complicating variables, and by using a cutting plane method where cuts are generated by solving the subproblem. The purpose of this masterclass is to introduce the basic Benders decomposition methodology, to present several computational refinements that have shown to improve performance, and to discuss some recent developments. ______________________________________________________________________________ 10:15am - 11:15am Session: Logic-Based Benders Decomposition (KC203) Cluster: CPAIOR Chair: John Hooker, Carnegie Mellon University Logic-Based Benders Decomposition John Hooker, Carnegie Mellon University, [email protected] This is a tutorial on logic-based Benders decomposition, which generalizes the classical Benders method so as to accommodate an arbitrary subproblem rather than only a linear or continuous nonlinear programming problem. This allows one to apply Benders profitably to any problem that simplifies or decouples when certain variables are -
SPARC Institutional Repository Checklist & Resource Guide
SPARC Institutional Repository Checklist & Resource Guide The Scholarly Publishing & Academic Resources Coalition 21 Dupont Circle • Washington, DC 20036 www.arl.org/sparc Prepared by Raym Crow, SPARC Senior Consultant SPARC Institutional Repository Checklist & Resource Guide Acknowledgements SPARC and the author wish to thank the many people whose comments have shaped this document. We would especially like to thank Chris Gutteridge of the University of Southampton and EPrints; Ed Sponsler and Kim Douglas of the Caltech Libraries; and MacKenzie Smith of the MIT Libraries and DSpace. The benefit of their experience and insight has improved this Guide immeasurably. Any errors or omissions that remain, however, are the sole responsibility of SPARC and the author. This document will be revised and updated on an ongoing basis as new information warrants. To comment on this document, please contact Raym Crow at [email protected]. SPARC Institutional Repository Checklist & Resource Guide Release 1.0 November 2002 © SPARC, 2002 Permission is granted to reproduce, distribute or electronically post copies of this work for nonprofit educational purposes, provided that the author, source, and copyright notices are included on each copy. This permission is in addition to the rights of reproduction granted under Sections 107, 108, and other provisions of the U.S. Copyright Act. These items may be further forwarded and distributed so long as the statement of copyright remains intact. All trademarks and service marks mentioned herein are the property of their respective owners. Page 2 of 51 SPARC Institutional Repository Checklist & Resource Guide TABLE OF CONTENTS INTRODUCTION.................................................................................................Page 5 The Institutional Repository................................................................................... 5 Document Purpose ................................................................................................. -
Persistent Identifiers
Network of Expertise in Digital Preservation Persistent Identifiers Reinhard Altenhöner Die Deutsche Bibliothek, Frankfurt am Main, Germany [email protected] Die Deutsche Bibliothek Chinese-European Workshop on Digital Preservation, Beijing July 14 – 16 2004 1 Network of Expertise in Digital Preservation Table of Contents Introduction: persistent identifiers URN: a standard in the world of internet Structure and realization(s) PI in Praxis: the project Epicur in DDB Conclusions/Summary Die Deutsche Bibliothek Chinese-European Workshop on Digital Preservation, Beijing July 14 – 16 2004 2 Network of Expertise in Digital Preservation Die Deutsche Bibliothek Chinese-European Workshop on Digital Preservation, Beijing July 14 – 16 2004 3 Network of Expertise in Digital Preservation Identification of cars Number plate Chassis number non stable reliable can be a fake persistent small functionality appropriate non global functionality opaque (resolution!) global transparent unique Die Deutsche Bibliothek Chinese-European Workshop on Digital Preservation, Beijing July 14 – 16 2004 4 Network of Expertise in Digital Preservation The daily experience Die Deutsche Bibliothek Chinese-European Workshop on Digital Preservation, Beijing July 14 – 16 2004 5 Network of Expertise in Digital Preservation Die Deutsche Bibliothek Chinese-European Workshop on Digital Preservation, Beijing July 14 – 16 2004 6 Network of Expertise in Digital Preservation Persistence in the WEB 16% links after 6 months (T.Dowling) 50% after 24 months (British