Book•
AMPL: A Modeling Language for Mathematical Programming
01 Jan 1993-
TL;DR: An efficient translator is implemented that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers.
Abstract: Practical large-scale mathematical programming involves more than just the application of an algorithm to minimize or maximize an objective function. Before any optimizing routine can be invoked, considerable effort must be expended to formulate the underlying model and to generate the requisite computational data structures. AMPL is a new language designed to make these steps easier and less error-prone. AMPL closely resembles the symbolic algebraic notation that many modelers use to describe mathematical programs, yet it is regular and formal enough to be processed by a computer system; it is particularly notable for the generality of its syntax and for the variety of its indexing operations. We have implemented an efficient translator that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers. Both the language and the translator admit straightforward extensions to more general mathematical programs that incorporate nonlinear expressions or discrete variables.
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01 Nov 2008TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
17,420 citations
Cites methods from "AMPL: A Modeling Language for Mathe..."
...We refer the reader to Dantzig [86] and Fourer, Gay, and Kernighan [112] for more comprehensive discussion of this issue....
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...Information about modeling techniques for various application areas can be found in Dantzig [86], Ahuja, Magnanti, and Orlin [1], Fourer, Gay, and Kernighan [112], Winston [308], and Rardin [262]....
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08 Feb 1999
TL;DR: Support vector machines for dynamic reconstruction of a chaotic system, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel.
Abstract: Introduction to support vector learning roadmap. Part 1 Theory: three remarks on the support vector method of function estimation, Vladimir Vapnik generalization performance of support vector machines and other pattern classifiers, Peter Bartlett and John Shawe-Taylor Bayesian voting schemes and large margin classifiers, Nello Cristianini and John Shawe-Taylor support vector machines, reproducing kernel Hilbert spaces, and randomized GACV, Grace Wahba geometry and invariance in kernel based methods, Christopher J.C. Burges on the annealed VC entropy for margin classifiers - a statistical mechanics study, Manfred Opper entropy numbers, operators and support vector kernels, Robert C. Williamson et al. Part 2 Implementations: solving the quadratic programming problem arising in support vector classification, Linda Kaufman making large-scale support vector machine learning practical, Thorsten Joachims fast training of support vector machines using sequential minimal optimization, John C. Platt. Part 3 Applications: support vector machines for dynamic reconstruction of a chaotic system, Davide Mattera and Simon Haykin using support vector machines for time series prediction, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel. Part 4 Extensions of the algorithm: reducing the run-time complexity in support vector machines, Edgar E. Osuna and Federico Girosi support vector regression with ANOVA decomposition kernels, Mark O. Stitson et al support vector density estimation, Jason Weston et al combining support vector and mathematical programming methods for classification, Bernhard Scholkopf et al.
5,506 citations
Cites methods or result from "AMPL: A Modeling Language for Mathe..."
...The AMPL code is available on request from the author athttp://www.math.rpi.edu/ bennek....
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...Our results are consistant with the statisticallearning theory results that incorporating working data improves generalizationwhen insu cient training information is available....
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...Using the mathematical programming modeling language AMPL (Fourer et al.,1993), we were able to express the problem in approximately thirty lines of codeplus a data le and solve it using CPLEX.3 If the 2-norm is used for marginmaximization, then the problem becomes a quadratic integer program....
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TL;DR: It is shown that performance profiles combine the best features of other tools for performance evaluation to create a single tool for benchmarking and comparing optimization software.
Abstract: We propose performance profiles — distribution functions for a performance metric — as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation.
3,729 citations
TL;DR: An SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems is discussed.
Abstract: Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse.
We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom (say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections (about 900 examples).
2,831 citations
TL;DR: This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.
Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.
2,056 citations
Cites methods from "AMPL: A Modeling Language for Mathe..."
...This design contrasts to the stack based VM used in e.g. the AMPL Solver Library [45]....
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...CasADi is an open-source software framework for numerical optimization, offering an alternative to conventional algebraic modeling languages such as AMPL [45], Pyomo [67] and JuMP [35]....
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...The first two examples introduce the optimization modeling approach in CasADi, which differs from that of conventional algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo....
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...CasADi is an open-source software for numerical optimization, offering an alternative to conventional algebraic modeling languages such as AMPL [50], Pyomo [69] and JUMP [40]....
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References
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Book•
01 Jan 1985TL;DR: Bjarne Stroustrup makes C even more accessible to those new to the language, while adding advanced information and techniques that even expert C programmers will find invaluable.
Abstract: From the Publisher:
Written by Bjarne Stroustrup, the creator of C, this is the world's most trusted and widely read book on C.
For this special hardcover edition, two new appendixes on locales and standard library exception safety have been added. The result is complete, authoritative coverage of the C language, its standard library, and key design techniques. Based on the ANSI/ISO C standard, The C Programming Language provides current and comprehensive coverage of all C language features and standard library components.
For example:
abstract classes as interfaces class hierarchies for object-oriented programming templates as the basis for type-safe generic software exceptions for regular error handling namespaces for modularity in large-scale software run-time type identification for loosely coupled systems the C subset of C for C compatibility and system-level work standard containers and algorithms standard strings, I/O streams, and numerics C compatibility, internationalization, and exception safety
Bjarne Stroustrup makes C even more accessible to those new to the language, while adding advanced information and techniques that even expert C programmers will find invaluable.
6,795 citations
01 Jan 1986
TL;DR: The C Programming Language as discussed by the authors provides a complete, authoritative coverage of the C language, its standard library, and key design techniques, as well as its locales and exception safety.
Abstract: From the Publisher:
Written by Bjarne Stroustrup, the creator of C, this is the world's most trusted and widely read book on C.
For this special hardcover edition, two new appendixes on locales and standard library exception safety have been added. The result is complete, authoritative coverage of the C language, its standard library, and key design techniques. Based on the ANSI/ISO C standard, The C Programming Language provides current and comprehensive coverage of all C language features and standard library components.
For example:
abstract classes as interfaces class hierarchies for object-oriented programming templates as the basis for type-safe generic software exceptions for regular error handling namespaces for modularity in large-scale software run-time type identification for loosely coupled systems the C subset of C for C compatibility and system-level work standard containers and algorithms standard strings, I/O streams, and numerics C compatibility, internationalization, and exception safety
Bjarne Stroustrup makes C even more accessible to those new to the language, while adding advanced information and techniques that even expert C programmers will find invaluable.
791 citations
01 Jan 1984
TL;DR: In this article, the authors describe the UNIX programming environment and philosophy in detail, including how to use the system, its components, and the programs, but also how these fit into the total environment.
Abstract: From the Publisher:
Designed for first-time and experienced users, this book describes the UNIX® programming environment and philosophy in detail. Readers will gain an understanding not only of how to use the system, its components, and the programs, but also how these fit into the total environment.
514 citations
Book•
01 Apr 1989
TL;DR: A translator is implemented that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers.
Abstract: Practical large-scale mathematical programming involves more than just the application of an algorithm to minimize or maximize an objective function. Before any optimizing routine can be invoked, considerable effort must be expended to formulate the underlying model and to generate the requisite computational data structures. AMPL is a new language designed to make these steps easier and less error-prone. AMPL closely resembles the symbolic algebraic notation that many modelers use to describe mathematical programs, yet it is regular and formal enough to be processed by a computer system; it is particularly notable for the generality of its syntax and for the variety of its indexing operations. We have implemented a translator that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers. Both the language and the translator admit straightforward extensions to more general mathematical programs that incorporate nonlinear expressions or discrete variables.
249 citations
01 Jan 1982
TL;DR: This paper describes the resulting development of a General Algebraic Modeling System (GAMS), which employs a rigorous algebraic representation of data and equations, coupled with relational database-type facilities, and draws comparisons to other modeling systems designed for large-scale linear programming problems.
Abstract: This article, On the Development of a General Algebraic Modeling System in a Strategic Planning Environment, was reprinted with permission from the 1982 volume of Mathematical Programming Study. It highlights and explains modeling activities at the World Bank. The Bank represents a strategic planning environment in which mathematical models have a potentially important role to play. Barriers to the effectiveness of models include extensive resource requirements, low reliability, and communication problems. In response, this paper examines requirements for successful modeling applications. It describes the resulting development of a General Algebraic Modeling System (GAMS), which employs a rigorous algebraic representation of data and equations, coupled with relational database-type facilities. The paper analyzes the data structure of this system in some detail, and draws comparisons to other modeling systems designed for large-scale linear programming problems. Selected aspects of the language are presented. The paper concludes with a case study of investment planning in the Egyptian Fertilizer Sector. In the case study, the model was used as a moderator, and was continuously modified as the planning process took place. GAMS was used as the basic modeling tool.
227 citations