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Xpress Nonlinear Manual This Material Is the Confidential, Proprietary, and Unpublished Property of Fair Isaac Corporation
R FICO Xpress Optimization Last update 01 May, 2018 version 33.01 FICO R Xpress Nonlinear Manual This material is the confidential, proprietary, and unpublished property of Fair Isaac Corporation. Receipt or possession of this material does not convey rights to divulge, reproduce, use, or allow others to use it without the specific written authorization of Fair Isaac Corporation and use must conform strictly to the license agreement. The information in this document is subject to change without notice. If you find any problems in this documentation, please report them to us in writing. Neither Fair Isaac Corporation nor its affiliates warrant that this documentation is error-free, nor are there any other warranties with respect to the documentation except as may be provided in the license agreement. ©1983–2018 Fair Isaac Corporation. All rights reserved. Permission to use this software and its documentation is governed by the software license agreement between the licensee and Fair Isaac Corporation (or its affiliate). Portions of the program may contain copyright of various authors and may be licensed under certain third-party licenses identified in the software, documentation, or both. In no event shall Fair Isaac Corporation or its affiliates be liable to any person for direct, indirect, special, incidental, or consequential damages, including lost profits, arising out of the use of this software and its documentation, even if Fair Isaac Corporation or its affiliates have been advised of the possibility of such damage. The rights and allocation of risk between the licensee and Fair Isaac Corporation (or its affiliates) are governed by the respective identified licenses in the software, documentation, or both. -
Julia, My New Friend for Computing and Optimization? Pierre Haessig, Lilian Besson
Julia, my new friend for computing and optimization? Pierre Haessig, Lilian Besson To cite this version: Pierre Haessig, Lilian Besson. Julia, my new friend for computing and optimization?. Master. France. 2018. cel-01830248 HAL Id: cel-01830248 https://hal.archives-ouvertes.fr/cel-01830248 Submitted on 4 Jul 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. « Julia, my new computing friend? » | 14 June 2018, IETR@Vannes | By: L. Besson & P. Haessig 1 « Julia, my New frieNd for computiNg aNd optimizatioN? » Intro to the Julia programming language, for MATLAB users Date: 14th of June 2018 Who: Lilian Besson & Pierre Haessig (SCEE & AUT team @ IETR / CentraleSupélec campus Rennes) « Julia, my new computing friend? » | 14 June 2018, IETR@Vannes | By: L. Besson & P. Haessig 2 AgeNda for today [30 miN] 1. What is Julia? [5 miN] 2. ComparisoN with MATLAB [5 miN] 3. Two examples of problems solved Julia [5 miN] 4. LoNger ex. oN optimizatioN with JuMP [13miN] 5. LiNks for more iNformatioN ? [2 miN] « Julia, my new computing friend? » | 14 June 2018, IETR@Vannes | By: L. Besson & P. Haessig 3 1. What is Julia ? Open-source and free programming language (MIT license) Developed since 2012 (creators: MIT researchers) Growing popularity worldwide, in research, data science, finance etc… Multi-platform: Windows, Mac OS X, GNU/Linux.. -
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. -
[20Pt]Algorithms for Constrained Optimization: [ 5Pt]
SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Algorithms for Constrained Optimization: The Benefits of General-purpose Software Michael Saunders MS&E and ICME, Stanford University California, USA 3rd AI+IoT Business Conference Shenzhen, China, April 25, 2019 Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 1/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SOL Systems Optimization Laboratory George Dantzig, Stanford University, 1974 Inventor of the Simplex Method Father of linear programming Large-scale optimization: Algorithms, software, applications Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 2/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SOL history 1974 Dantzig and Cottle start SOL 1974{78 John Tomlin, LP/MIP expert 1974{2005 Alan Manne, nonlinear economic models 1975{76 MS, MINOS first version 1979{87 Philip Gill, Walter Murray, MS, Margaret Wright (Gang of 4!) 1989{ Gerd Infanger, stochastic optimization 1979{ Walter Murray, MS, many students 2002{ Yinyu Ye, optimization algorithms, especially interior methods This week! UC Berkeley opened George B. Dantzig Auditorium Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 3/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Optimization problems Minimize an objective function subject to constraints: 0 x 1 min '(x) st ` ≤ @ Ax A ≤ u c(x) x variables 0 1 A matrix c1(x) B . C c(x) nonlinear functions @ . A c (x) `; u bounds m Optimization -
Numericaloptimization
Numerical Optimization Alberto Bemporad http://cse.lab.imtlucca.it/~bemporad/teaching/numopt Academic year 2020-2021 Course objectives Solve complex decision problems by using numerical optimization Application domains: • Finance, management science, economics (portfolio optimization, business analytics, investment plans, resource allocation, logistics, ...) • Engineering (engineering design, process optimization, embedded control, ...) • Artificial intelligence (machine learning, data science, autonomous driving, ...) • Myriads of other applications (transportation, smart grids, water networks, sports scheduling, health-care, oil & gas, space, ...) ©2021 A. Bemporad - Numerical Optimization 2/102 Course objectives What this course is about: • How to formulate a decision problem as a numerical optimization problem? (modeling) • Which numerical algorithm is most appropriate to solve the problem? (algorithms) • What’s the theory behind the algorithm? (theory) ©2021 A. Bemporad - Numerical Optimization 3/102 Course contents • Optimization modeling – Linear models – Convex models • Optimization theory – Optimality conditions, sensitivity analysis – Duality • Optimization algorithms – Basics of numerical linear algebra – Convex programming – Nonlinear programming ©2021 A. Bemporad - Numerical Optimization 4/102 References i ©2021 A. Bemporad - Numerical Optimization 5/102 Other references • Stephen Boyd’s “Convex Optimization” courses at Stanford: http://ee364a.stanford.edu http://ee364b.stanford.edu • Lieven Vandenberghe’s courses at UCLA: http://www.seas.ucla.edu/~vandenbe/ • For more tutorials/books see http://plato.asu.edu/sub/tutorials.html ©2021 A. Bemporad - Numerical Optimization 6/102 Optimization modeling What is optimization? • Optimization = assign values to a set of decision variables so to optimize a certain objective function • Example: Which is the best velocity to minimize fuel consumption ? fuel [ℓ/km] velocity [km/h] 0 30 60 90 120 160 ©2021 A. -
TOMLAB –Unique Features for Optimization in MATLAB
TOMLAB –Unique Features for Optimization in MATLAB Bad Honnef, Germany October 15, 2004 Kenneth Holmström Tomlab Optimization AB Västerås, Sweden [email protected] ´ Professor in Optimization Department of Mathematics and Physics Mälardalen University, Sweden http://tomlab.biz Outline of the talk • The TOMLAB Optimization Environment – Background and history – Technology available • Optimization in TOMLAB • Tests on customer supplied large-scale optimization examples • Customer cases, embedded solutions, consultant work • Business perspective • Box-bounded global non-convex optimization • Summary http://tomlab.biz Background • MATLAB – a high-level language for mathematical calculations, distributed by MathWorks Inc. • Matlab can be extended by Toolboxes that adds to the features in the software, e.g.: finance, statistics, control, and optimization • Why develop the TOMLAB Optimization Environment? – A uniform approach to optimization didn’t exist in MATLAB – Good optimization solvers were missing – Large-scale optimization was non-existent in MATLAB – Other toolboxes needed robust and fast optimization – Technical advantages from the MATLAB languages • Fast algorithm development and modeling of applied optimization problems • Many built in functions (ODE, linear algebra, …) • GUIdevelopmentfast • Interfaceable with C, Fortran, Java code http://tomlab.biz History of Tomlab • President and founder: Professor Kenneth Holmström • The company founded 1986, Development started 1989 • Two toolboxes NLPLIB och OPERA by 1995 • Integrated format for optimization 1996 • TOMLAB introduced, ISMP97 in Lausanne 1997 • TOMLAB v1.0 distributed for free until summer 1999 • TOMLAB v2.0 first commercial version fall 1999 • TOMLAB starting sales from web site March 2000 • TOMLAB v3.0 expanded with external solvers /SOL spring 2001 • Dash Optimization Ltd’s XpressMP added in TOMLAB fall 2001 • Tomlab Optimization Inc. -
Specifying “Logical” Conditions in AMPL Optimization Models
Specifying “Logical” Conditions in AMPL Optimization Models Robert Fourer AMPL Optimization www.ampl.com — 773-336-AMPL INFORMS Annual Meeting Phoenix, Arizona — 14-17 October 2012 Session SA15, Software Demonstrations Robert Fourer, Logical Conditions in AMPL INFORMS Annual Meeting — 14-17 Oct 2012 — Session SA15, Software Demonstrations 1 New and Forthcoming Developments in the AMPL Modeling Language and System Optimization modelers are often stymied by the complications of converting problem logic into algebraic constraints suitable for solvers. The AMPL modeling language thus allows various logical conditions to be described directly. Additionally a new interface to the ILOG CP solver handles logic in a natural way not requiring conventional transformations. Robert Fourer, Logical Conditions in AMPL INFORMS Annual Meeting — 14-17 Oct 2012 — Session SA15, Software Demonstrations 2 AMPL News Free AMPL book chapters AMPL for Courses Extended function library Extended support for “logical” conditions AMPL driver for CPLEX Opt Studio “Concert” C++ interface Support for ILOG CP constraint programming solver Support for “logical” constraints in CPLEX INFORMS Impact Prize to . Originators of AIMMS, AMPL, GAMS, LINDO, MPL Awards presented Sunday 8:30-9:45, Conv Ctr West 101 Doors close 8:45! Robert Fourer, Logical Conditions in AMPL INFORMS Annual Meeting — 14-17 Oct 2012 — Session SA15, Software Demonstrations 3 AMPL Book Chapters now free for download www.ampl.com/BOOK/download.html Bound copies remain available purchase from usual -
AIMMS 4 Release Notes
AIMMS 4 Release Notes Visit our web site www.aimms.com for regular updates Contents Contents 2 1 System Requirements 3 1.1 Hardware and operating system requirements ......... 3 1.2 ODBC and OLE DB database connectivity issues ........ 4 1.3 Viewing help files and documentation .............. 5 2 Installation Instructions 7 2.1 Installation instructions ....................... 7 2.2 Solver availability per platform ................... 8 2.3 Aimms licensing ............................ 9 2.3.1 Personal and machine nodelocks ............. 9 2.3.2 Installing an Aimms license ................ 12 2.3.3 Managing Aimms licenses ................. 14 2.3.4 Location of license files ................... 15 2.4 OpenSSL license ............................ 17 3 Project Conversion Instructions 20 3.1 Conversion of projects developed in Aimms 3.13 and before 20 3.2 Conversionof Aimms 3 projects to Aimms 4 ........... 22 3.2.1 Data management changes in Aimms 4.0 ........ 24 4 Getting Support 27 4.1 Reporting a problem ......................... 27 4.2 Known and reported issues ..................... 28 5 Release Notes 29 What’s new in Aimms 4 ........................ 29 Chapter 1 System Requirements This chapter discusses the system requirements necessary to run the various System components of your Win32 Aimms 4 system successfully. When a particular requirements requirement involves the installation of additional system software compo- nents, or an update thereof, the (optional) installation of such components will be part of the Aimms installation procedure. 1.1 Hardware and operating system requirements The following list provides the minimum hardware requirements to run your Hardware Aimms 4 system. requirements 1.6 Ghz or higher x86 or x64 processor XGA display adapter and monitor 1 Gb RAM 1 Gb free disk space Note, however, that performance depends on model size and type and can vary. -
Spatially Explicit Techno-Economic Optimisation Modelling of UK Heating Futures
Spatially explicit techno-economic optimisation modelling of UK heating futures A thesis submitted in fulfilment of the requirements for the Degree of Doctor of Philosophy UCL Energy Institute University College London Date: 3rd April 2013 Candidate: Francis Li Supervisors: Robert Lowe, Mark Barrett I, Francis Li, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Francis Li, 3rd April 2013 2 For Eugenia 3 Abstract This thesis describes the use of a spatially explicit model to investigate the economies of scale associated with district heating technologies and consequently, their future technical potential when compared against individual building heating. Existing energy system models used for informing UK technology policy do not employ high enough spatial resolutions to map district heating potential at the individual settlement level. At the same time, the major precedent studies on UK district heating potential have not explored future scenarios out to 2050 and have a number of relevant low-carbon heat supply technologies absent from their analyses. This has resulted in cognitive dissonance in UK energy policy whereby district heating is often simultaneously acknowledged as both highly desirable in the near term but ultimately lacking any long term future. The Settlement Energy Demand System Optimiser (SEDSO) builds on key techno-economic studies from the last decade to further investigate this policy challenge. SEDSO can be distinguished from other models used for investigating UK heat decarbonisation by employing a unique combination of extensive spatial detail, technical modelling which captures key cost-related nonlinearities, and a least-cost constrained optimisation approach to technology selection. -
AIMMS 4 Linux Release Notes
AIMMS 4 Portable component Linux Intel version Release Notes for Linux Visit our web site www.aimms.com for regular updates Contents Contents 2 1 System Overview of the Intel Linux Aimms Component 3 1.1 Hardware and operating system requirements ......... 3 1.2 Feature comparison with the Win32/Win64 version ...... 3 2 Installation and Usage 5 2.1 Installation instructions ....................... 5 2.2 Solver availability per platform ................... 6 2.3 Licensing ................................ 6 2.4 Usage of the portable component ................. 10 2.5 The Aimms command line tool ................... 10 3 Getting Support 13 3.1 Reporting a problem ......................... 13 3.2 Known and reported issues ..................... 14 4 Release Notes 15 What’s new in Aimms 4 ........................ 15 Chapter 1 System Overview of the Intel Linux Aimms Component This chapter discusses the system requirements necessary to run the portable System Intel Linux Aimms component. The chapter also contains a feature comparison overview with the regular Windows version of Aimms. 1.1 Hardware and operating system requirements The following list of hardware and software requirements applies to the por- Hardware table Intel x64 Linux Aimms 4 component release. requirements Linux x64 Intel x64 compatible system Centos 6, Red Hat 6, or Ubuntu 12.04 Linux operating system 1 Gb RAM 1 Gb free disk space Note, however, that performance depends on model size and type and can Performance vary. It can also be affected by the number of other applications that are running concurrently with Aimms. In cases of a (regular) performance drop of either Aimms or other applications you are advised to install sufficiently additional RAM. -
Robert Fourer, David M. Gay INFORMS Annual Meeting
AMPL New Solver Support in the AMPL Modeling Language Robert Fourer, David M. Gay AMPL Optimization LLC, www.ampl.com Department of Industrial Engineering & Management Sciences, Northwestern University Sandia National Laboratories INFORMS Annual Meeting Pittsburgh, Pennsylvania, November 5-8, 2006 Robert Fourer, New Solver Support in the AMPL Modeling Language INFORMS Annual Meeting, November 5-8, 2006 1 AMPL What it is . A modeling language for optimization A system to support optimization modeling What I’ll cover . Brief examples, briefer history Recent developments . ¾ 64-bit versions ¾ floating license manager ¾ AMPL Studio graphical interface & Windows COM objects Solver support ¾ new KNITRO 5.1 features ¾ new CPLEX 10.1 features Robert Fourer, New Solver Support in the AMPL Modeling Language INFORMS Annual Meeting, November 5-8, 2006 2 Ex 1: Airline Fleet Assignment set FLEETS; set CITIES; set TIMES circular; set FLEET_LEGS within {f in FLEETS, c1 in CITIES, t1 in TIMES, c2 in CITIES, t2 in TIMES: c1 <> c2 and t1 <> t2}; # (f,c1,t1,c2,t2) represents the availability of fleet f # to cover the leg that leaves c1 at t1 and # whose arrival time plus turnaround time at c2 is t2 param leg_cost {FLEET_LEGS} >= 0; param fleet_size {FLEETS} >= 0; Robert Fourer, New Solver Support in the AMPL Modeling Language INFORMS Annual Meeting, November 5-8, 2006 3 Ex 1: Derived Sets set LEGS := setof {(f,c1,t1,c2,t2) in FLEET_LEGS} (c1,t1,c2,t2); # the set of all legs that can be covered by some fleet set SERV_CITIES {f in FLEETS} := union {(f,c1,c2,t1,t2) -
Notes 1: Introduction to Optimization Models
Notes 1: Introduction to Optimization Models IND E 599 September 29, 2010 IND E 599 Notes 1 Slide 1 Course Objectives I Survey of optimization models and formulations, with focus on modeling, not on algorithms I Include a variety of applications, such as, industrial, mechanical, civil and electrical engineering, financial optimization models, health care systems, environmental ecology, and forestry I Include many types of optimization models, such as, linear programming, integer programming, quadratic assignment problem, nonlinear convex problems and black-box models I Include many common formulations, such as, facility location, vehicle routing, job shop scheduling, flow shop scheduling, production scheduling (min make span, min max lateness), knapsack/multi-knapsack, traveling salesman, capacitated assignment problem, set covering/packing, network flow, shortest path, and max flow. IND E 599 Notes 1 Slide 2 Tentative Topics Each topic is an introduction to what could be a complete course: 1. basic linear models (LP) with sensitivity analysis 2. integer models (IP), such as the assignment problem, knapsack problem and the traveling salesman problem 3. mixed integer formulations 4. quadratic assignment problems 5. include uncertainty with chance-constraints, stochastic programming scenario-based formulations, and robust optimization 6. multi-objective formulations 7. nonlinear formulations, as often found in engineering design 8. brief introduction to constraint logic programming 9. brief introduction to dynamic programming IND E 599 Notes 1 Slide 3 Computer Software I Catalyst Tools (https://catalyst.uw.edu/) I AIMMS - optimization software (http://www.aimms.com/) Ming Fang - AIMMS software consultant IND E 599 Notes 1 Slide 4 What is Mathematical Programming? Mathematical programming refers to \programming" as a \planning" activity: as in I linear programming (LP) I integer programming (IP) I mixed integer linear programming (MILP) I non-linear programming (NLP) \Optimization" is becoming more common, e.g.