Specifying “Logical” Conditions in AMPL Optimization Models
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University of California, San Diego
UNIVERSITY OF CALIFORNIA, SAN DIEGO Computational Methods for Parameter Estimation in Nonlinear Models A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics with a Specialization in Computational Physics by Bryan Andrew Toth Committee in charge: Professor Henry D. I. Abarbanel, Chair Professor Philip Gill Professor Julius Kuti Professor Gabriel Silva Professor Frank Wuerthwein 2011 Copyright Bryan Andrew Toth, 2011 All rights reserved. The dissertation of Bryan Andrew Toth is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2011 iii DEDICATION To my grandparents, August and Virginia Toth and Willem and Jane Keur, who helped put me on a lifelong path of learning. iv EPIGRAPH An Expert: One who knows more and more about less and less, until eventually he knows everything about nothing. |Source Unknown v TABLE OF CONTENTS Signature Page . iii Dedication . iv Epigraph . v Table of Contents . vi List of Figures . ix List of Tables . x Acknowledgements . xi Vita and Publications . xii Abstract of the Dissertation . xiii Chapter 1 Introduction . 1 1.1 Dynamical Systems . 1 1.1.1 Linear and Nonlinear Dynamics . 2 1.1.2 Chaos . 4 1.1.3 Synchronization . 6 1.2 Parameter Estimation . 8 1.2.1 Kalman Filters . 8 1.2.2 Variational Methods . 9 1.2.3 Parameter Estimation in Nonlinear Systems . 9 1.3 Dissertation Preview . 10 Chapter 2 Dynamical State and Parameter Estimation . 11 2.1 Introduction . 11 2.2 DSPE Overview . 11 2.3 Formulation . 12 2.3.1 Least Squares Minimization . -
Multi-Objective Optimization of Unidirectional Non-Isolated Dc/Dcconverters
MULTI-OBJECTIVE OPTIMIZATION OF UNIDIRECTIONAL NON-ISOLATED DC/DC CONVERTERS by Andrija Stupar A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Edward S. Rogers Department of Electrical and Computer Engineering University of Toronto © Copyright 2017 by Andrija Stupar Abstract Multi-Objective Optimization of Unidirectional Non-Isolated DC/DC Converters Andrija Stupar Doctor of Philosophy Graduate Department of Edward S. Rogers Department of Electrical and Computer Engineering University of Toronto 2017 Engineers have to fulfill multiple requirements and strive towards often competing goals while designing power electronic systems. This can be an analytically complex and computationally intensive task since the relationship between the parameters of a system’s design space is not always obvious. Furthermore, a number of possible solutions to a particular problem may exist. To find an optimal system, many different possible designs must be evaluated. Literature on power electronics optimization focuses on the modeling and design of partic- ular converters, with little thought given to the mathematical formulation of the optimization problem. Therefore, converter optimization has generally been a slow process, with exhaus- tive search, the execution time of which is exponential in the number of design variables, the prevalent approach. In this thesis, geometric programming (GP), a type of convex optimization, the execution time of which is polynomial in the number of design variables, is proposed and demonstrated as an efficient and comprehensive framework for the multi-objective optimization of non-isolated unidirectional DC/DC converters. A GP model of multilevel flying capacitor step-down convert- ers is developed and experimentally verified on a 15-to-3.3 V, 9.9 W discrete prototype, with sets of loss-volume Pareto optimal designs generated in under one minute. -
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.. -
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. -
Click to Edit Master Title Style
Click to edit Master title style MINLP with Combined Interior Point and Active Set Methods Jose L. Mojica Adam D. Lewis John D. Hedengren Brigham Young University INFORM 2013, Minneapolis, MN Presentation Overview NLP Benchmarking Hock-Schittkowski Dynamic optimization Biological models Combining Interior Point and Active Set MINLP Benchmarking MacMINLP MINLP Model Predictive Control Chiller Thermal Energy Storage Unmanned Aerial Systems Future Developments Oct 9, 2013 APMonitor.com APOPT.com Brigham Young University Overview of Benchmark Testing NLP Benchmark Testing 1 1 2 3 3 min J (x, y,u) APOPT , BPOPT , IPOPT , SNOPT , MINOS x Problem characteristics: s.t. 0 f , x, y,u t Hock Schittkowski, Dynamic Opt, SBML 0 g(x, y,u) Nonlinear Programming (NLP) Differential Algebraic Equations (DAEs) 0 h(x, y,u) n m APMonitor Modeling Language x, y u MINLP Benchmark Testing min J (x, y,u, z) 1 1 2 APOPT , BPOPT , BONMIN x s.t. 0 f , x, y,u, z Problem characteristics: t MacMINLP, Industrial Test Set 0 g(x, y,u, z) Mixed Integer Nonlinear Programming (MINLP) 0 h(x, y,u, z) Mixed Integer Differential Algebraic Equations (MIDAEs) x, y n u m z m APMonitor & AMPL Modeling Language 1–APS, LLC 2–EPL, 3–SBS, Inc. Oct 9, 2013 APMonitor.com APOPT.com Brigham Young University NLP Benchmark – Summary (494) 100 90 80 APOPT+BPOPT APOPT 70 1.0 BPOPT 1.0 60 IPOPT 3.10 IPOPT 50 2.3 SNOPT Percentage (%) 6.1 40 Benchmark Results MINOS 494 Problems 5.5 30 20 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Not worse than 2 times slower than -
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. -
Standard Price List
Regular price list April 2021 (Download PDF ) This price list includes the required base module and a number of optional solvers. The prices shown are for unrestricted, perpetual named single user licenses on a specific platform (Windows, Linux, Mac OS X), please ask for additional platforms. Prices Module Price (USD) GAMS/Base Module (required) 3,200 MIRO Connector 3,200 GAMS/Secure - encrypted Work Files Option 3,200 Solver Price (USD) GAMS/ALPHAECP 1 1,600 GAMS/ANTIGONE 1 (requires the presence of a GAMS/CPLEX and a GAMS/SNOPT or GAMS/CONOPT license, 3,200 includes GAMS/GLOMIQO) GAMS/BARON 1 (for details please follow this link ) 3,200 GAMS/CONOPT (includes CONOPT 4 ) 3,200 GAMS/CPLEX 9,600 GAMS/DECIS 1 (requires presence of a GAMS/CPLEX or a GAMS/MINOS license) 9,600 GAMS/DICOPT 1 1,600 GAMS/GLOMIQO 1 (requires presence of a GAMS/CPLEX and a GAMS/SNOPT or GAMS/CONOPT license) 1,600 GAMS/IPOPTH (includes HSL-routines, for details please follow this link ) 3,200 GAMS/KNITRO 4,800 GAMS/LGO 2 1,600 GAMS/LINDO (includes GAMS/LINDOGLOBAL with no size restrictions) 12,800 GAMS/LINDOGLOBAL 2 (requires the presence of a GAMS/CONOPT license) 1,600 GAMS/MINOS 3,200 GAMS/MOSEK 3,200 GAMS/MPSGE 1 3,200 GAMS/MSNLP 1 (includes LSGRG2) 1,600 GAMS/ODHeuristic (requires the presence of a GAMS/CPLEX or a GAMS/CPLEX-link license) 3,200 GAMS/PATH (includes GAMS/PATHNLP) 3,200 GAMS/SBB 1 1,600 GAMS/SCIP 1 (includes GAMS/SOPLEX) 3,200 GAMS/SNOPT 3,200 GAMS/XPRESS-MINLP (includes GAMS/XPRESS-MIP and GAMS/XPRESS-NLP) 12,800 GAMS/XPRESS-MIP (everything but general nonlinear equations) 9,600 GAMS/XPRESS-NLP (everything but discrete variables) 6,400 Solver-Links Price (USD) GAMS/CPLEX Link 3,200 GAMS/GUROBI Link 3,200 Solver-Links Price (USD) GAMS/MOSEK Link 1,600 GAMS/XPRESS Link 3,200 General information The GAMS Base Module includes the GAMS Language Compiler, GAMS-APIs, and many utilities . -
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. -
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. -
AIMMS Modeling Guide - Linear Programming Tricks
AIMMS Modeling Guide - Linear Programming Tricks This file contains only one chapter of the book. For a free download of the complete book in pdf format, please visit www.aimms.com. Aimms 4 Copyright c 1993–2018 by AIMMS B.V. All rights reserved. AIMMS B.V. AIMMS Inc. Diakenhuisweg 29-35 11711 SE 8th Street 2033 AP Haarlem Suite 303 The Netherlands Bellevue, WA 98005 Tel.: +31 23 5511512 USA Tel.: +1 425 458 4024 AIMMS Pte. Ltd. AIMMS 55 Market Street #10-00 SOHO Fuxing Plaza No.388 Singapore 048941 Building D-71, Level 3 Tel.: +65 6521 2827 Madang Road, Huangpu District Shanghai 200025 China Tel.: ++86 21 5309 8733 Email: [email protected] WWW: www.aimms.com Aimms is a registered trademark of AIMMS B.V. IBM ILOG CPLEX and CPLEX is a registered trademark of IBM Corporation. GUROBI is a registered trademark of Gurobi Optimization, Inc. Knitro is a registered trademark of Artelys. Windows and Excel are registered trademarks of Microsoft Corporation. TEX, LATEX, and AMS-LATEX are trademarks of the American Mathematical Society. Lucida is a registered trademark of Bigelow & Holmes Inc. Acrobat is a registered trademark of Adobe Systems Inc. Other brands and their products are trademarks of their respective holders. Information in this document is subject to change without notice and does not represent a commitment on the part of AIMMS B.V. The software described in this document is furnished under a license agreement and may only be used and copied in accordance with the terms of the agreement. The documentation may not, in whole or in part, be copied, photocopied, reproduced, translated, or reduced to any electronic medium or machine-readable form without prior consent, in writing, from AIMMS B.V. -
Open Source Tools for Optimization in Python
Open Source Tools for Optimization in Python Ted Ralphs Sage Days Workshop IMA, Minneapolis, MN, 21 August 2017 T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Outline 1 Introduction 2 COIN-OR 3 Modeling Software 4 Python-based Modeling Tools PuLP/DipPy CyLP yaposib Pyomo T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Outline 1 Introduction 2 COIN-OR 3 Modeling Software 4 Python-based Modeling Tools PuLP/DipPy CyLP yaposib Pyomo T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Caveats and Motivation Caveats I have no idea about the background of the audience. The talk may be either too basic or too advanced. Why am I here? I’m not a Sage developer or user (yet!). I’m hoping this will be a chance to get more involved in Sage development. Please ask lots of questions so as to guide me in what to dive into! T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Mathematical Optimization Mathematical optimization provides a formal language for describing and analyzing optimization problems. Elements of the model: Decision variables Constraints Objective Function Parameters and Data The general form of a mathematical optimization problem is: min or max f (x) (1) 8 9 < ≤ = s.t. gi(x) = bi (2) : ≥ ; x 2 X (3) where X ⊆ Rn might be a discrete set. T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Types of Mathematical Optimization Problems The type of a mathematical optimization problem is determined primarily by The form of the objective and the constraints.