DOCSLIB.ORG

N Rapid Development of an Open-Source Minlp Solver With

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
N Rapid Development of an Open-Source Minlp Solver With 75 o N O PTIMA Mathematical Programming Society Newsletter DECEMBER 2007 Rapid Development of an Open-source Minlp Solver with COIN-OR Pierre Bonami, John J. Forrest, Jon Lee and Andreas Wächter Abstract • Csdp, Dfo, Ipopt, LaGO, and Svm- QP are solvers for different types of We describe the rapid development of Nonlinear Optimization (semidefinite, Bonmin (Basic Open-source Nonlinear derivative-free, general large-scale Mixed INteger programming) using the interior point, global optimization, QP community and components of COIN- solver for support vector machines) OR (COmputational INfrastructure • CoinMP, FlopC++, GAMSlinks, for Operations Research). NLPAPI, Osi, OS and Smi are problem 1. Introduction modeling and interface tools. Even more, COIN-OR has become the As famous examples like Linux have platform that facilitates the collaboration proven, open-source communities of optimization researchers to start entirely can produce rapidly-developing high- new projects, exploring and developing new quality software, often competitive with algorithmic ideas, by providing both a sound expensive commercial solutions. COIN- software basis that can be re-used, as well as OR (COmputational INfrastructure the technical forum to coordinate the effort. for Operations Research), originally In order to clarify a common founded by IBM in 2000 and a non-profit misconception, we want to emphasize that foundation since 2004, provides such the term “open source” does not simply refer a platform for us optimization folks. to software that is made available to some Since its conception, a number of users in source-code format. According optimization-algorithm implementations to the definition put forth by the non- and related software projects have been profit corporation Open Source Initiative contributed to COIN-OR. From a web (OSI) [26], a number of conditions must server hosted by INFORMS, at the URL be met for a software license to be an www.COIN-OR.org, COIN-OR offers “open-source” license, including the right online repositories for sharing source code, for free distribution and usage (including web sites with information, documentation for commercial purposes), as well as the and bug tracking systems, as well as mailing right to modify the code. There are many lists for users and developers. Many of OSI-certified open-source licenses. The the optimization codes have been used one preferred on COIN-OR is the CPL extensively by academics and in commercial (Common Public License [12]), which was products. chosen for its very liberal terms. Currently, COIN-OR hosts many In this article, we tell the on-going success optimization-related codes: story of one such project. In 2004, IBM and • Clp, DyLP, and Vol are solvers Carnegie Mellon University initiated a joint for Linear Programming study aimed at Mixed Integer Nonlinear • Bcp, Cbc, Cgl, Cops, and Symphony Programming (MINLP), with the goal of are solvers, frameworks and tools releasing the resulting software under the for (serial and parallel) Mixed- CPL on COIN-OR. In 2006, within a Integer Linear Programming, new Open Collaborative Research (OCR) 75George Nemhauser's Contributions 5 MPS Chair’s Optima Column 6 Prizes and Conferences 7 OPT I M A 7 5 DECEMBER 2007 page 2 initiative at IBM, this relationship with g(x) ≤ 0, sub-domain, problems can be much harder CMU was extended. This OCR program x ∈ Rn-k × Zk, than the MILP counterparts. A main reason builds on the Open Collaboration Principles where f : Rn a R and g : Rn a Rm are is that in the space of the natural variables, established in 2005 by IBM and eleven twice continuously differentiable. the solution of a relaxation may be well other institutions to accelerate innovation MINLP is the mother of all deterministic inside the interior of the feasible region, and foster open-source research. optimization problems. Many business and so the cutting planes that have been so Besides the joint activity of CMU and and engineering optimization problems successful for MILP may have very limited IBM, the subject of MINLP has received a are naturally formulated as mathematical value (see [24], for example). lot of recent attention. For example, programs involving both discrete and If the relaxation of the MINLP problem • The 2006 Beale-Orchard Hays Prize continuous variables, as often decisions is not convex, we are really in a different for Excellence in Computational have to be made that involve making world. There are several approaches. There Mathematical Programming was discrete decisions (e.g., yes/no) and setting are ad hoc heuristics, which suffer from awarded by the Mathematical continuous levels (e.g., flowrates). Natural being well suited to only very specific Programming Society to Nick Sahinidis phenomena often involve relationships models (see [23], for example). There is the and Mohit Tawarmalani for their between variables which, while often possibility of taking methods designed for work on global optimization which smooth, may be rather nonlinear. Accurate problems having convex relaxations and culminated in their software Baron [3, models need to allow for all of these. heuristically adapting them to problems 27]; global optimization is one of the key A common approach to such problems that do not satisfy this restriction (e.g., approaches to MINLP, and Baron can is to reformulate them as Mixed Integer the branch-and-bound option of Bonmin; be directly applied to MINLP problems. Linear Programming (MILP) problems, see [7]). There is the approach of global • The 2006 CORE Lecture Series usually through the use of piecewise-linear optimization typified by the method of consisted of a series of lectures by functions approximating the true functions. spatial branch-and-bound wherein one Robert Weismantel on MINLP. In the presence of non-convexity, this leads repeatedly subdivides the feasible region, Our goal was to develop algorithms to the introduction of additional binary with the goal of producing better and and software for this important class of variables or non-standard branching rules. better convex under-estimators (e.g., Baron; problems. We undertook to carry this out in The inaccuracies that are introduced and see [28]). Finally, there is the approach of the context of COIN-OR. Our original goal the added computational effort induced systematically remodeling a broad subclass was to use existing software components of by accommodating the piecewise-linear of MINLP problems as MILPs using COIN-OR to produce a simple NLP-based functions may make the value of such a specialized techniques (e.g., see [16] for such branch-and-bound code aimed at MINLP solution approach rather limited. a method using linked ordered sets) problems that have convex relaxations. As Another approach is to relax the MINLP we progressed, we expanded our goal and to an NLP, apply an NLP solver, and then 3. Building Blocks developed instantiations of several MINLP use some heuristic method to reach a nearby As MINLP combines the worlds of methods, aimed mostly at problems having feasible point that respects the integrality MILP and of NLP, a logical start for convex relaxations. We were able to carry restrictions. Just as for MILP, this technique the Bonmin project was to look at the this out rather quickly, as we had at our is not very robust, often leading to very poor existing codes and libraries in COIN- disposal the source code to manage a solutions. OR related to MILP and NLP and to branch-and-bound tree and to solve MILP The alternative to methods that are based see how they could be integrated. and NLP subproblems. strictly on either MILP and NLP is to Cbc (Coin Branch and Cut) is a powerful, In Section 2, we describe the setting develop methods that are directly aimed at industrial-strength branch-and-cut code of MINLP. In Section 3, we discuss the MINLP formulations. In effect, one shifts for MILP problems. It is a component COIN-OR NLP solver Ipopt and the some of the burden from the modeler to of COIN-OR, and it uses several other COIN-OR MILP solver Cbc, which were the solution software. Still, just as we know components of COIN-OR. It uses Clp (the the starting points of our implementation. from MILP and NLP, there are always Coin Linear Programming solver) through In Section 4, we describe the capabilities significant issues that cannot be ignored the Osi (Open Solver Interface) library. The of our MINLP solver Bonmin (Basic by a modeler who seeks to solve difficult Osi is a layer used to insulate an application Open-source Nonlinear Mixed INteger instances. that makes use of an LP solver from the programming) and how we constructed It is useful to first consider methods specific LP solver employed. Clp includes it using other components of COIN-OR. that are aimed at MINLP problems primal and dual simplex solvers as well as Finally, in Section 5, we discuss ongoing having convex relaxations. In this sub- an interior-point method. As a full-fledged and future plans for Bonmin. domain, there are natural methods that branch-and-cut code, Cbc strengthens generalize MILP methods (e.g., branch- relaxations through use of the COIN Cgl 2. MINLP and-bound, using NLP subproblems) as (Cut Generation Library), accommodates well as more sophisticated methods like We consider MINLP problems of the form different node-selection and branching rules outer approximation (see [13]), generalized min f(x) (e.g., via pseudocosts and strong branching), Bender's decomposition (see [18]) and hybrid and allows for SOS Type-1 and Type-2 methods (see [8], for example). Even in this Date: November 2, 2007. modeling and branching. Cgl includes a OPT I M A 7 5 DECEMBER 2007 page 3 wide variety of cutting-plane generators (including: knapsack cover, odd hole, flow cover, lift and project, Gomory, reduce and split, and MIR).
Load more

Recommended publications
  • Algorithmic System Design Under Consideration of Dynamic Processes
    Algorithmic System Design under Consideration of Dynamic Processes Vom Fachbereich Maschinenbau an der Technischen Universit¨atDarmstadt zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften (Dr.-Ing.) genehmigte Dissertation vorgelegt von Dipl.-Phys. Lena Charlotte Altherr aus Karlsruhe Berichterstatter: Prof. Dr.-Ing. Peter F. Pelz Mitberichterstatter: Prof. Dr. rer. nat. Ulf Lorenz Tag der Einreichung: 19.04.2016 Tag der m¨undlichen Pr¨ufung: 24.05.2016 Darmstadt 2016 D 17 Vorwort des Herausgebers Kontext Die Produkt- und Systementwicklung hat die Aufgabe technische Systeme so zu gestalten, dass eine gewünschte Systemfunktion erfüllt wird. Mögliche System- funktionen sind z.B. Schwingungen zu dämpfen, Wasser in einem Siedlungsgebiet zu verteilen oder die Kühlung eines Rechenzentrums. Wir Ingenieure reduzieren dabei die Komplexität eines Systems, indem wir dieses gedanklich in überschaubare Baugruppen oder Komponenten zerlegen und diese für sich in Robustheit und Effizienz verbessern. In der Kriegsführung wurde dieses Prinzip bereits 500 v. Chr. als „Teile und herrsche Prinzip“ durch Meister Sun in seinem Buch „Die Kunst der Kriegsführung“ beschrieben. Das Denken in Schnitten ist wesentlich für das Verständnis von Systemen: „Das wichtigste Werkzeug des Ingenieurs ist die Schere“. Das Zusammenwirken der Komponenten führt anschließend zu der gewünschten Systemfunktion. Während die Funktion eines technischen Systems i.d.R. nicht verhan- delbar ist, ist jedoch verhandelbar mit welchem Aufwand diese erfüllt wird und mit welcher Verfügbarkeit sie gewährleistet wird. Aufwand und Verfügbarkeit sind dabei gegensätzlich. Der Aufwand bemisst z.B. die Emission von Kohlendioxid, den Energieverbrauch, den Materialverbrauch, … die „total cost of ownership“. Die Verfügbarkeit bemisst die Ausfallzeiten, Lebensdauer oder Laufleistung. Die Gesell- schaft stellt sich zunehmend die Frage, wie eine Funktion bei minimalem Aufwand und maximaler Verfügbarkeit realisiert werden kann.
    [Show full text]
  • 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]
    [Show full text]
  • Basic Polyhedral Theory 3
    BASIC POLYHEDRAL THEORY VOLKER KAIBEL A polyhedron is the intersection of finitely many affine halfspaces, where an affine halfspace is a set ≤ n H (a, β)= x Ê : a, x β { ∈ ≤ } n n n Ê Ê for some a Ê and β (here, a, x = j=1 ajxj denotes the standard scalar product on ). Thus, every∈ polyhedron is∈ the set ≤ n P (A, b)= x Ê : Ax b { ∈ ≤ } m×n of feasible solutions to a system Ax b of linear inequalities for some matrix A Ê and some m ≤ n ′ ′ ∈ Ê vector b Ê . Clearly, all sets x : Ax b, A x = b are polyhedra as well, as the system A′x = b∈′ of linear equations is equivalent{ ∈ the system≤ A′x }b′, A′x b′ of linear inequalities. A bounded polyhedron is called a polytope (where bounded≤ means− that≤ there − is a bound which no coordinate of any point in the polyhedron exceeds in absolute value). Polyhedra are of great importance for Operations Research, because they are not only the sets of feasible solutions to Linear Programs (LP), for which we have beautiful duality results and both practically and theoretically efficient algorithms, but even the solution of (Mixed) Integer Linear Pro- gramming (MILP) problems can be reduced to linear optimization problems over polyhedra. This relationship to a large extent forms the backbone of the extremely successful story of (Mixed) Integer Linear Programming and Combinatorial Optimization over the last few decades. In Section 1, we review those parts of the general theory of polyhedra that are most important with respect to optimization questions, while in Section 2 we treat concepts that are particularly relevant for Integer Programming.
    [Show full text]
  • 1. Introduction: Learning About Operations Research
    1. Introduction: Learning about Operations Research IRV LUSTIG: So hi, my name's Irv Lustig from Princeton Consultants and today, I'm privileged to interview George Nemhauser, who is currently a distinguished professor at the Georgia Institute of Technology. So thank you, George, for joining us today and let's get started. GEORGE NEMHAUSER: Oh, you're most welcome. I'm really looking forward to it. IRV LUSTIG: All right. So tell me, when did you first learn about operations research? GEORGE NEMHAUSER: So basically, I am a chemical engineer. And I think it was the summer between when I graduated with a Bachelor's degree in Chemical Engineering and the fall, when I was going to go off to graduate school at Northwestern for Chemical Engineering, I had a job with the research department of Allied Chemical. And there was a guy-- I think he was my supervisor who was working there-- who told me he was taking a part-time degree at Princeton and he was studying things like linear programming and game theory and I think maybe Kuhn, Tucker conditions, And he told me about this kind of stuff and I thought, wow, this is really interesting stuff, much more interesting than what I'm doing in chemical engineering. So when I got to Northwestern, as a first-year graduate student in Chemical Engineering, I had one elective course. And I looked and there was this new course called Operations Research and it included linear programming and game theory and stuff like that. I said, that's it.
    [Show full text]
  • Branch-And-Bound Strategies for Dynamic Programming
    LIBRARY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY C7. WORKING PAPER ALFRED P. SLOAN SCHOOL OF MANAGEMENT BRANCH-AND-BOUND STRATEGIES FOR DYNAMIC PROGRAMMING Thomas L. Morin* and Roy E. Marsten** WP 750-74ooREVISED May 1975 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 50 MEMORIAL DRIVE CAMBRIDGE, MASSACHUSETTS 02139 BRANCH-AND-BOUND STRATEGIES FOR DYNAMIC PROGRAMMING Thomas L. Morin* and Roy E. Mar St en** WP 750-74floREVISED May 1975 *Northwestern University, Evanston, Illinois **Massachusetts Institute of Technology Alfred P. Sloan School of Management, Cambridge, Massachusetts ABSTRACT This paper shows how branch -and -bound methods can be used to reduce storage and, possibly, computational requirements in discrete dynamic programs. Relaxations and fathoming cjriteria are used to identify and to eliminate states whose corresponding subpolicies could not lead to optimal policies. The general dynamic programming/branch- and-bound approach is applied to the traveling -salesman problem and the nonlinear knapsack problem. The reported computational experience de- monstrates the dramatic savings in both computer storage and computa- tional requirements which were effected utilizing the hybrid approach. Consider the following functional equation of dynamic programming for additive costs: = {TT(y',d) (y = (P. - f(y) min + f ') lT(y ' ,d) y] , y € y.) (1) d € D with the boundary condition f(yo) = ko (2) in which, Q is the finite nonempty state space; y- € fi is the initial state; d € D is a decision, where D is the finite nonempty set of decisions; T: n X D — n is the transition mapping, where T(y',d) is the state that is tt; -• reached when decision d is applied at state y ; Q x D IR is the cost function, where TT(y',d) is the incremental cost that is incurred when de- cision d is applied at state y'; k_ 6 IR is the initial cost incurred in the initial state y_; and in (2) we make the convenient but unnecessary assump- tion that return to the initial state is not possible.
    [Show full text]
  • A New Column for Optima Structure Prediction and Global Optimization
    76 o N O PTIMA Mathematical Programming Society Newsletter MARCH 2008 Structure Prediction and A new column Global Optimization for Optima by Alberto Caprara Marco Locatelli Andrea Lodi Dip. Informatica, Univ. di Torino (Italy) Katya Scheinberg Fabio Schoen Dip. Sistemi e Informatica, Univ. di Firenze (Italy) This is the first issue of 2008 and it is a very dense one with a Scientific February 26, 2008 contribution on computational biology, some announcements, reports of “Every attempt to employ mathematical methods in the study of chemical conferences and events, the MPS Chairs questions must be considered profoundly irrational and contrary to the spirit in chemistry. If mathematical analysis should ever hold a prominent place Column. Thus, the extra space is limited in chemistry — an aberration which is happily almost impossible — it but we like to use few additional lines would occasion a rapid and widespread degeneration of that science.” for introducing a new feature we are — Auguste Comte particularly happy with. Starting with Cours de philosophie positive issue 76 there will be a Discussion Column whose content is tightly related “It is not yet clear whether optimization is indeed useful for biology — surely biology has been very useful for optimization” to the Scientific contribution, with ­ — Alberto Caprara a purpose of making every issue of private communication Optima recognizable through a special topic. The Discussion Column will take the form of a comment on the Scientific 1 Introduction contribution from some experts in Many new problem domains arose from the study of biological and the field other than the authors or chemical systems and several mathematical programming models an interview/discussion of a couple as well as algorithms have been developed.
    [Show full text]
  • Mathematical Programming Society Newsletter
    69 o N O PTIMA Mathematical Programming Society Newsletter JANUARY2003 69 Primal Integer Programming 2 mindsharpener 8 gallimaufry 10 OPTIMA69 JANUARY 2003 PAGE 2 Primal Integer Programming Robert Weismantel Faculty of Mathematics, University of Magdeburg Universitatsplatz 2, D-39106 Magdeburg, Germany [email protected] September 17, 2002 Primal integer programming is an area of Let us begin by recalling that all the problem specific cuts such as facet-defining cuts discrete optimization that -- in a broad sense -- algorithmic schemes applied to integer for the TSP in [18]. To the best of our includes the theory and algorithms related to programming problems without a-priori knowledge, a method of this type for Integer augmenting feasible integer solutions or knowledge about the structure of the side Programming has first been suggested by Ben- verifying optimality of feasible integer points. constraints resort to the power of linear Israel and Charnes [3]. They employed the fact This theory naturally provides an algorithmic programming duality. that for any feasible solution of an integer scheme that one might regard as a generic form Dual type algorithms start solving a linear program optimality can be proven by solving a of a primal integer programming algorithm: programming relaxation of the problem, subproblem arising from the non-basic columns First detect an integer point in a given domain typically with the dual simplex method. In the of a primal feasible simplex tableau. Various of discrete points. Then verify whether this course of the algorithm one maintains as an specializations and variants of a primal cutting point is an optimal solution with respect to a invariant both primal and dual feasibility of the plane algorithm were later given by Young [21, specific objective function, and if not, find solution of the relaxation.
    [Show full text]
  • Twenty-Eighth Annual Report of The
    National Science Foundation Twenty-Eighth Annual Report for Fiscal Year 1978 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $3.25 Stock Number 038-000-00407-7 Letter of Transmittal Washington, D.C. DEAR MR. PRESIDENT: I have the honor to transmit herewith the Annual Report for Fiscal Year 1978 of the National Science Foundation for submission to the Congress as required by the National Science Foundation Act of 1950. Respectfully, Richard C. Atkinson Director, National Science foundation The Honorable The President of ihe United Slates Contents Page Director's Statement vii Mathematical and Physical Sciences, and Engineering 1 Physics 2 Chemistry 6 Mathematical and Computer Sciences 10 Engineering 16 Materials Research 21 Astronomical, Atmospheric, Earth, and Ocean Sciences 29 Astronomy 31 Atmospheric Sciences 39 Earth Sciences 45 Ocean Sciences 51 Polar Programs 56 Biological, Behavioral, and Social Sciences 61 Physiology, Cellular, and Molecular Biology 62 Behavioral and Neural Sciences 67 Environmental Biology 69 Social Sciences 73 Science Education '77 Science Education Resources Improvement 77 Science Education Development and Research 81 Scientific Personnel Improvement 86 Science and Society 91 Applied Science and Research Applications 97 Problem Analysis 98 Integrated Basic Research 98 Applied Research 99 Problem-Focused Research Applications 101 Intergovernmental Science and Public Technology 105 Scientific, Technological, and International Affairs 109 Policy Research and Analysis 110 Science Resources Studies 112 NSF Planning and Evaluation 115 Information Science and Technology 116 International Programs , 118 Appendices A. National Science Board, NSF Staff, Advisory Committees and Panels 121 B. Patents and Inventions Resulting from Activities Supported by the National Science Foundation 138 C.
    [Show full text]
  • From the Editor WHATS INSIDE
    Volume 6 Number 1 March 2012 International Federation of Operational Research Societies NEWS ISSN 2223-4373 WHATS INSIDE From the Editor 2 Editorial . 2011 Accomplishments - IFORS and OR publishing and A Taste of 2012 3 Publications . Elise del Rosario <[email protected]> - ITOR Features Tutorials We used to dedicate one issue of IFORS News to the - Tutorial: The importance of pricing decisions Annual Report. This year, we have a full issue that com- plements the 2011 Annual Report. The year had been 5 Developing Countries . a most productive one for the Administrative Commit- tee, as can be gleaned from the President Dominique de Werra’s summary of - A Star for ORiON the activities undertaken for the year. - Locals Support First OR Meeting in Nepal - From the DC Section Editor: On the Activities continued on into 2012, as you can see from the OR Schools con- ORSN Conference ducted in Africa and Brazil and those being planned for in Ukraine and Por- - OR tools have huge potential tugal. It is always very refreshing to see these young people, all enthusiastic about OR and benefiting from the various programs made available to them 8 Conferences . by IFORS and other sponsors. - Portugal Hosts the First ICORES - OR Luminaries Grace Peruvian Conference Conferences that were held within ALIO, EURO and APORS are covered. IFORS was well represented in the conferences that happened in Peru, Por- 10 OR Schools . tugal and Nepal. I met the Developing Countries Section editor Arabinda Tripathy at the Nepal conference, and his perspectives on that conference - IFORS Sponsors OR School in Africa are here printed.
    [Show full text]
  • George Dantzig's Contributions to Integer Programming
    Takustraße 7 Konrad-Zuse-Zentrum D-14195 Berlin-Dahlem fur¨ Informationstechnik Berlin Germany MARTIN GROTSCHEL¨ AND GEORGE L. NEMHAUSER George Dantzig’s contributions to integer programming ZIB-Report 07-39 (November 2007) George Dantzig's Contributions to Integer Programming Martin GrÄotschel Konrad-Zuse-Zentrum fÄurInformationstechnik Berlin (ZIB), Matheon, and TU Berlin, Germany [email protected] George L. Nemhauser School of Industrial and Systems Engineering Georgia Institute of Technology USA [email protected] Abstract This paper reviews George Dantzig's contribution to integer programming, espe- cially his seminal work with Fulkerson and Johnson on the traveling salesman problem. 1 Introduction George Dantzig wrote only a few papers on integer programming, including two on integer programming modeling [4, 5]; speci¯cally, how a variety of nonlinear and nonconvex opti- mization problems could be formulated as mixed-integer programs with 0-1 variables. For example, he presented the use of 0-1 variables to model ¯xed charges and variable upper bound constraints, semi-continuous variables, and nonconvex piecewise linear functions. In [5] he also proposed a very simple cutting plane for separating a fractional basic optimal solution from the convex hull of integer solutions in a pure integer program with nonnegative variables. The cut simply says that at least one of the nonbasic variables must be a positive integer, i.e., the sum of the nonbasic variables is at least one. While this is not a very strong cut, since it does not yield a ¯nitely convergent algorithm [10], a slightly tightened version of it does yield a ¯nite cutting plane algorithm [2].
    [Show full text]
  • ISMP BP Front
    Conference Program 1 TABLE OF CONTENTS Welcome from the Chair . 2 Schedule of Daily Events & Sessions . 3 20TH INTERNATIONAL SYMPOSIUM ON Speaker Information . 5 MATHEMATICAL PROGRAMMING August 23-28, 2009 Social Events & Excursions . 6 Chicago, Illinois, USA Internet Access . 7 Opening Session & Prizes . 8 Area Map . 9 PROGRAM ORGANIZING COMMITTEE COMMITTEE Exhibitors . 10 Chair Mihai Anitescu John R. Birge Argonne National Lab Plenary & Semi-Plenary Sessions . 12 University of Chicago USA Track Schedule . 17 USA John R. Birge Karen Aardal University of Chicago Floor Plans & Maps . 22 Centrum Wiskunde & USA Informatica Michael Ferris Cluster Chairs . 24 The Netherlands University of Wisconsin- Michael Ferris Madison Technical Sessions University of Wisconsin- USA Monday . 25 Madison Jeff Linderoth USA University of Wisconsin- Tuesday . 49 Michael Goemans Madison Wednesday . 74 Massachusetts Institute of USA Thursday . 98 Technology Todd Munson USA Argonne National Lab Friday . 121 Michael Jünger USA Universität zu Köln Jorge Nocedal Session Chair Index . 137 Germany Northwestern University Masakazu Kojima USA Author Index . 139 Tok yo Institute of Technology Jong-Shi Pang Session Index . 147 Japan University of Illinois at Urbana- Rolf Möhring Champaign Advertisers Technische Universität Berlin USA World Scientific . .150 Germany Stephen J. Wright Andy Philpott University of Wisconsin- IOS Press . .151 University of Auckland Madison OptiRisk Systems . .152 New Zealand USA Claudia Sagastizábal Taylor & Francis . .153 CEPEL LINDO Systems . .154 Brazil Springer . .155 Stephen J. Wright University of Wisconsin- Mosek . .156 Madison USA Sponsors . Back Cover Yinyu Ye Stanford University USA 2 Welcome from the Chair On behalf of the Organizing Committee and The University of Chicago, I The University of Chicago welcome you to ISMP 2009, the 20th International Symposium on Booth School of Business Mathematical Programming.
    [Show full text]
  • Integer Programming
    50 Years of Integer Programming 1958–2008 Michael Junger¨ · Thomas Liebling · Denis Naddef · George Nemhauser · William Pulleyblank · Gerhard Reinelt · Giovanni Rinaldi · Laurence Wolsey Editors 50 Years of Integer Programming 1958–2008 From the Early Years to the State-of-the-Art 123 Editors Michael Junger¨ Thomas M. Liebling Universitat¨ zu Koln¨ Ecole Polytechnique Fed´ erale´ de Lausanne Institut fur¨ Informatik Faculte´ des Sciences de Base Pohligstraße 1 Institut de Mathematiques´ 50969 Koln¨ Station 8 Germany 1015 Lausanne [email protected] Switzerland Denis Naddef thomas.liebling@epfl.ch Grenoble Institute of Technology - Ensimag George L. Nemhauser Laboratoire G-SCOP Industrial and Systems Engineering 46 avenue Felix´ Viallet Georgia Institute of Technology 38031 Grenoble Cedex 1 Atlanta, GA 30332-0205 France USA [email protected] [email protected] William R. Pulleyblank Gerhard Reinelt IBM Corporation Universitat¨ Heidelberg 294 Route 100 Institut fur¨ Informatik Somers NY 10589 Im Neuenheimer Feld 368 USA 69120 Heidelberg [email protected] Germany Giovanni Rinaldi [email protected] CNR - Istituto di Analisi dei Sistemi Laurence A. Wolsey ed Informatica “Antonio Ruberti” Universite´ Catholique de Louvain Viale Manzoni, 30 Center for Operations Research and 00185 Roma Econometrics (CORE) Italy voie du Roman Pays 34 [email protected] 1348 Louvain-la-Neuve Belgium [email protected] ISBN 978-3-540-68274-5 e-ISBN 978-3-540-68279-0 DOI 10.1007/978-3-540-68279-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009938839 Mathematics Subject Classification (2000): 01-02, 01-06, 01-08, 65K05, 65K10, 90-01, 90-02, 90-03, 90-06, 90-08, 90C05, 90C06, 90C08, 90C09, 90C10, 90C11, 90C20, 90C22, 90C27, 90C30, 90C35, 90C46, 90C47, 90C57, 90C59, 90C60, 90C90 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright.
    [Show full text]