Academic Price List April 2021 (Download PDF ) This Price List Includes the Required Base Module and a Number of Optional Solvers
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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 . -
How to Use Your Favorite MIP Solver: Modeling, Solving, Cannibalizing
How to use your favorite MIP Solver: modeling, solving, cannibalizing Andrea Lodi University of Bologna, Italy [email protected] January-February, 2012 @ Universit¨atWien A. Lodi, How to use your favorite MIP Solver Setting • We consider a general Mixed Integer Program in the form: T maxfc x : Ax ≤ b; x ≥ 0; xj 2 Z; 8j 2 Ig (1) where matrix A does not have a special structure. A. Lodi, How to use your favorite MIP Solver 1 Setting • We consider a general Mixed Integer Program in the form: T maxfc x : Ax ≤ b; x ≥ 0; xj 2 Z; 8j 2 Ig (1) where matrix A does not have a special structure. • Thus, the problem is solved through branch-and-bound and the bounds are computed by iteratively solving the LP relaxations through a general-purpose LP solver. A. Lodi, How to use your favorite MIP Solver 1 Setting • We consider a general Mixed Integer Program in the form: T maxfc x : Ax ≤ b; x ≥ 0; xj 2 Z; 8j 2 Ig (1) where matrix A does not have a special structure. • Thus, the problem is solved through branch-and-bound and the bounds are computed by iteratively solving the LP relaxations through a general-purpose LP solver. • The course basically covers the MIP but we will try to discuss when possible how crucial is the LP component (the engine), and how much the whole framework is built on top the capability of effectively solving LPs. • Roughly speaking, using the LP computation as a tool, MIP solvers integrate the branch-and-bound and the cutting plane algorithms through variations of the general branch-and-cut scheme [Padberg & Rinaldi 1987] developed in the context of the Traveling Salesman Problem (TSP). -
Process Optimization
Process Optimization Mathematical Programming and Optimization of Multi-Plant Operations and Process Design Ralph W. Pike Director, Minerals Processing Research Institute Horton Professor of Chemical Engineering Louisiana State University Department of Chemical Engineering, Lamar University, April, 10, 2007 Process Optimization • Typical Industrial Problems • Mathematical Programming Software • Mathematical Basis for Optimization • Lagrange Multipliers and the Simplex Algorithm • Generalized Reduced Gradient Algorithm • On-Line Optimization • Mixed Integer Programming and the Branch and Bound Algorithm • Chemical Production Complex Optimization New Results • Using one computer language to write and run a program in another language • Cumulative probability distribution instead of an optimal point using Monte Carlo simulation for a multi-criteria, mixed integer nonlinear programming problem • Global optimization Design vs. Operations • Optimal Design −Uses flowsheet simulators and SQP – Heuristics for a design, a superstructure, an optimal design • Optimal Operations – On-line optimization – Plant optimal scheduling – Corporate supply chain optimization Plant Problem Size Contact Alkylation Ethylene 3,200 TPD 15,000 BPD 200 million lb/yr Units 14 76 ~200 Streams 35 110 ~4,000 Constraints Equality 761 1,579 ~400,000 Inequality 28 50 ~10,000 Variables Measured 43 125 ~300 Unmeasured 732 1,509 ~10,000 Parameters 11 64 ~100 Optimization Programming Languages • GAMS - General Algebraic Modeling System • LINDO - Widely used in business applications -
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 -
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 -
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 . -
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. -
Co-Optimization of Transmission and Other Supply Resources
Co-optimization of Transmission and Other Supply Resources September, 2013 Illinois Institute of Technology Iowa State University Johns Hopkins University Purdue University West Virginia University For EISPC and NARUC Funded by the U.S Department of Energy Co-optimization of Transmission and Other Supply Resources prepared for Eastern Interconnection States’ Planning Council and National Association of Regulatory Utility Commissioners prepared by Dr. Andrew (Lu) Liu, Purdue University Dr. Benjamin H. Hobbs and Jonathan Ho, Johns Hopkins University Dr. James D. McCalley and Venkat Krishnan, Iowa State University Dr. Mohammad Shahidehpour, Illinois Institute of Technology Dr. Qipeng P. Zheng, University of Central Florida Acknowledgement: This material is based upon work supported by the Department of Energy, National Energy Technology Laboratory, under Award Number DE-OE0000316. The project team would like to thank Bob Pauley, Doug Gotham and Stan Hadley as well as the EISPC and NARUC organizations, for their support throughout this project. Patrick Sullivan of NREL provided crucial perspectives, advice, and resources during the project. We would also like to acknowledge inputs on earlier versions of our work by members of NARUC’s Studies and Whitepaper Workgroup. The earlier versions as well benefited from the editorial assistance provided by Jingjie Xiao, a former PhD student with the School of Industrial Engineering at Purdue University, and her generous efforts are greatly appreciated. In addition, the team gratefully acknowledge the generous and timely assistance of several organizations that have provided important background information on transmission planning, including but not limited to: Parveen Baig, Iowa Utilities Board Jaeseok Choi, Gyeongsang National University, South Korea Bruce Fardanesh, New York Power Authority Flora Flydt, ATC Ian Grant, TVA Bruce Hamilton, Smart Grid Network Ben Harrison, Duke Energy Michael Henderson, ISO New England Len Januzik, Quanta Technology David Kelley, SPP Raymond Kershaw, ITC Holdings Corp. -
MODELING LANGUAGES in MATHEMATICAL OPTIMIZATION Applied Optimization Volume 88
MODELING LANGUAGES IN MATHEMATICAL OPTIMIZATION Applied Optimization Volume 88 Series Editors: Panos M. Pardalos University o/Florida, U.S.A. Donald W. Hearn University o/Florida, U.S.A. MODELING LANGUAGES IN MATHEMATICAL OPTIMIZATION Edited by JOSEF KALLRATH BASF AG, GVC/S (Scientific Computing), 0-67056 Ludwigshafen, Germany Dept. of Astronomy, Univ. of Florida, Gainesville, FL 32611 Kluwer Academic Publishers Boston/DordrechtiLondon Distributors for North, Central and South America: Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA Telephone (781) 871-6600 Fax (781) 871-6528 E-Mail <[email protected]> Distributors for all other countries: Kluwer Academic Publishers Group Post Office Box 322 3300 AlI Dordrecht, THE NETHERLANDS Telephone 31 78 6576 000 Fax 31 786576474 E-Mail <[email protected]> .t Electronic Services <http://www.wkap.nl> Library of Congress Cataloging-in-Publication Kallrath, Josef Modeling Languages in Mathematical Optimization ISBN-13: 978-1-4613-7945-4 e-ISBN-13:978-1-4613 -0215 - 5 DOl: 10.1007/978-1-4613-0215-5 Copyright © 2004 by Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 2004 All rights reserved. No part ofthis pUblication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permission ofthe publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permissions for books published in the USA: P"§.;r.m.i.§J?i..QD.§.@:w.k~p" ..,.g.Qm Permissions for books published in Europe: [email protected] Printed on acid-free paper. -
Download Classic LINDO User's Manual
LINDO User’s Manual LINDO Systems, Inc. 1415 North Dayton Street, Chicago, Illinois 60622 Phone: (312)988-7422 Fax: (312)988-9065 E-mail: [email protected] WWW: http://www.lindo.com COPYRIGHT LINDO software and its related documentation are copyrighted. You may not copy the LINDO software or related documentation except in the manner authorized in the related documentation or with the written permission of LINDO systems, Inc. TRADEMARKS LINGO is a trademark, and LINDO and What’sBest! are registered trademarks, of LINDO Systems, Inc. Other product and company names mentioned herein are the property of their respective owners. DISCLAIMER LINDO Systems, Inc. warrants that on the date of receipt of your payment, the disk enclosed in the disk envelope contains an accurate reproduction of the LINDO software and that the copy of the related documentation is accurately reproduced. Due to the inherent complexity of computer programs and computer models, the LINDO software may not be completely free of errors. You are advised to verify your answers before basing decisions on them. NEITHER LINDO SYSTEMS, INC. NOR ANYONE ELSE ASSOCIATED IN THE CREATION, PRODUCTION, OR DISTRIBUTION OF THE LINDO SOFTWARE MAKES ANY OTHER EXPRESSED WARRANTIES REGARDING THE DISKS OR DOCUMENTATION AND MAKES NO WARRANTIES AT ALL, EITHER EXPRESSED OR IMPLIED, REGARDING THE LINDO SOFTWARE, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE OR OTHERWISE. Further, LINDO Systems, Inc. reserves the right to revise this software and related documentation and make changes to the content hereof without obligation to notify any person of such revisions or changes. -
GEKKO Documentation Release 1.0.1
GEKKO Documentation Release 1.0.1 Logan Beal, John Hedengren Aug 31, 2021 Contents 1 Overview 1 2 Installation 3 3 Project Support 5 4 Citing GEKKO 7 5 Contents 9 6 Overview of GEKKO 89 Index 91 i ii CHAPTER 1 Overview GEKKO is a Python package for machine learning and optimization of mixed-integer and differential algebraic equa- tions. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include parameter regression, data reconciliation, real-time optimization, dynamic simulation, and nonlinear predictive control. GEKKO is an object-oriented Python library to facilitate local execution of APMonitor. More of the backend details are available at What does GEKKO do? and in the GEKKO Journal Article. Example applications are available to get started with GEKKO. 1 GEKKO Documentation, Release 1.0.1 2 Chapter 1. Overview CHAPTER 2 Installation A pip package is available: pip install gekko Use the —-user option to install if there is a permission error because Python is installed for all users and the account lacks administrative priviledge. The most recent version is 0.2. You can upgrade from the command line with the upgrade flag: pip install--upgrade gekko Another method is to install in a Jupyter notebook with !pip install gekko or with Python code, although this is not the preferred method: try: from pip import main as pipmain except: from pip._internal import main as pipmain pipmain(['install','gekko']) 3 GEKKO Documentation, Release 1.0.1 4 Chapter 2. Installation CHAPTER 3 Project Support There are GEKKO tutorials and documentation in: • GitHub Repository (examples folder) • Dynamic Optimization Course • APMonitor Documentation • GEKKO Documentation • 18 Example Applications with Videos For project specific help, search in the GEKKO topic tags on StackOverflow. -
Largest Small N-Polygons: Numerical Results and Conjectured Optima
Largest Small n-Polygons: Numerical Results and Conjectured Optima János D. Pintér Department of Industrial and Systems Engineering Lehigh University, Bethlehem, PA, USA [email protected] Abstract LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for all even values 6 n 80, using the AMPL model development environment with the LGO nonlinear solver engine option. Our results compare favorably to the results obtained by other researchers who solved the problem using exact approaches (for 6 n 16), or general purpose numerical optimization software (for selected values from the range 6 n 100) using various local nonlinear solvers. Based on the results obtained, we also provide a regression model based estimate of the optimal area sequence {A(n)} for n 6. Key words Largest Small Polygons Mathematical Model Analytical and Numerical Solution Approaches AMPL Modeling Environment LGO Solver Suite For Nonlinear Optimization AMPL-LGO Numerical Results Comparison to Earlier Results Regression Model Based Optimum Estimates 1 Introduction The diameter of a (convex planar) polygon is defined as the maximal distance among the distances measured between all vertex pairs. In other words, the diameter of the polygon is the length of its longest diagonal. The largest small polygon with n vertices is the polygon of unit diameter that has maximal area. For any given integer n 3, we will refer to this polygon as LSP(n) with area A(n).