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Author: Jacob Elliot Mattingley Publisher: Stanford University ISBN: Category : Languages : en Pages : 123
Book Description
Convex optimization is widely used, in many fields, but is nearly always constrained to problems solved in a few minutes or seconds, and even then, nearly always with a human in the loop. The advent of parser-solvers has made convex optimization simpler and more accessible, and greatly increased the number of people using convex optimization. Most current applications, however, are for the design of systems or analysis of data. It is possible to use convex optimization for real-time or embedded applications, where the optimization solver is a part of a larger system. Here, the optimization algorithm must find solutions much faster than a generic solver, and often has a hard, real-time deadline. Use in embedded applications additionally means that the solver cannot fail, and must be robust even in the presence of relatively poor quality data. For ease of embedding, the solver should be simple, and have minimal dependencies on external libraries. Convex optimization has been successfully applied in such settings in the past. However, they have usually necessitated a custom, hand-written solver. This requires signficant time and expertise, and has been a major factor preventing the adoption of convex optimization in embedded applications. This work describes the implementation and use of a prototype code generator for convex optimization, CVXGEN, that creates high-speed solvers automatically. Using the principles of disciplined convex programming, CVXGEN allows the user to describe an optimization problem in a convenient, high-level language, then receive code for compilation into an extremely fast, robust, embeddable solver.
Author: Jacob Elliot Mattingley Publisher: Stanford University ISBN: Category : Languages : en Pages : 123
Book Description
Convex optimization is widely used, in many fields, but is nearly always constrained to problems solved in a few minutes or seconds, and even then, nearly always with a human in the loop. The advent of parser-solvers has made convex optimization simpler and more accessible, and greatly increased the number of people using convex optimization. Most current applications, however, are for the design of systems or analysis of data. It is possible to use convex optimization for real-time or embedded applications, where the optimization solver is a part of a larger system. Here, the optimization algorithm must find solutions much faster than a generic solver, and often has a hard, real-time deadline. Use in embedded applications additionally means that the solver cannot fail, and must be robust even in the presence of relatively poor quality data. For ease of embedding, the solver should be simple, and have minimal dependencies on external libraries. Convex optimization has been successfully applied in such settings in the past. However, they have usually necessitated a custom, hand-written solver. This requires signficant time and expertise, and has been a major factor preventing the adoption of convex optimization in embedded applications. This work describes the implementation and use of a prototype code generator for convex optimization, CVXGEN, that creates high-speed solvers automatically. Using the principles of disciplined convex programming, CVXGEN allows the user to describe an optimization problem in a convenient, high-level language, then receive code for compilation into an extremely fast, robust, embeddable solver.
Author: Jacob Elliot Mattingley Publisher: ISBN: Category : Languages : en Pages :
Book Description
Convex optimization is widely used, in many fields, but is nearly always constrained to problems solved in a few minutes or seconds, and even then, nearly always with a human in the loop. The advent of parser-solvers has made convex optimization simpler and more accessible, and greatly increased the number of people using convex optimization. Most current applications, however, are for the design of systems or analysis of data. It is possible to use convex optimization for real-time or embedded applications, where the optimization solver is a part of a larger system. Here, the optimization algorithm must find solutions much faster than a generic solver, and often has a hard, real-time deadline. Use in embedded applications additionally means that the solver cannot fail, and must be robust even in the presence of relatively poor quality data. For ease of embedding, the solver should be simple, and have minimal dependencies on external libraries. Convex optimization has been successfully applied in such settings in the past. However, they have usually necessitated a custom, hand-written solver. This requires signficant time and expertise, and has been a major factor preventing the adoption of convex optimization in embedded applications. This work describes the implementation and use of a prototype code generator for convex optimization, CVXGEN, that creates high-speed solvers automatically. Using the principles of disciplined convex programming, CVXGEN allows the user to describe an optimization problem in a convenient, high-level language, then receive code for compilation into an extremely fast, robust, embeddable solver.
Author: Peter Marwedel Publisher: Springer Science & Business Media ISBN: 1461523230 Category : Computers Languages : en Pages : 298
Book Description
Modern electronics is driven by the explosive growth of digital communications and multi-media technology. A basic challenge is to design first-time-right complex digital systems, that meet stringent constraints on performance and power dissipation. In order to combine this growing system complexity with an increasingly short time-to-market, new system design technologies are emerging based on the paradigm of embedded programmable processors. This concept introduces modularity, flexibility and re-use in the electronic system design process. However, its success will critically depend on the availability of efficient and reliable CAD tools to design, programme and verify the functionality of embedded processors. Recently, new research efforts emerged on the edge between software compilation and hardware synthesis, to develop high-quality code generation tools for embedded processors. Code Generation for Embedded Systems provides a survey of these new developments. Although not limited to these targets, the main emphasis is on code generation for modern DSP processors. Important themes covered by the book include: the scope of general purpose versus application-specific processors, machine code quality for embedded applications, retargetability of the code generation process, machine description formalisms, and code generation methodologies. Code Generation for Embedded Systems is the essential introduction to this fast developing field of research for students, researchers, and practitioners alike.
Author: Aharon Ben-Tal Publisher: SIAM ISBN: 9780898718829 Category : Technology & Engineering Languages : en Pages : 504
Book Description
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Author: Li Li Publisher: Springer ISBN: 3662463563 Category : Business & Economics Languages : en Pages : 150
Book Description
This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems. All derivation processes are presented in detail to aid in comprehension. The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice.
Author: Yurii Nesterov Publisher: SIAM ISBN: 9781611970791 Category : Mathematics Languages : en Pages : 414
Book Description
Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Author: Rainer Leupers Publisher: Springer Science & Business Media ISBN: 1475731698 Category : Computers Languages : en Pages : 218
Book Description
The building blocks of today's and future embedded systems are complex intellectual property components, or cores, many of which are programmable processors. Traditionally, these embedded processors mostly have been pro grammed in assembly languages due to efficiency reasons. This implies time consuming programming, extensive debugging, and low code portability. The requirements of short time-to-market and dependability of embedded systems are obviously much better met by using high-level language (e.g. C) compil ers instead of assembly. However, the use of C compilers frequently incurs a code quality overhead as compared to manually written assembly programs. Due to the need for efficient embedded systems, this overhead must be very low in order to make compilers useful in practice. In turn, this requires new compiler techniques that take the specific constraints in embedded system de sign into account. An example are the specialized architectures of recent DSP and multimedia processors, which are not yet sufficiently exploited by existing compilers.
Author: Eric Chu Publisher: ISBN: Category : Languages : en Pages :
Book Description
Convex optimization is widely used in many areas of engineering science such as control theory, statistics and machine learning, and image and signal processing. There are, however, several barriers to the use of convex optimization in everyday engineering: solvers for convex optimization in general require specialized knowledge to code, and in order to solve problems, users must typically perform tedious manual transformations before calling a solver. This problem is exacerbated when problem sizes become extremely large. In this thesis, we investigate tools and methods to address these two issues in the context of large-scale convex optimization. In particular, we develop technology to handle very large problems, including a large-scale solver and a tool to model potentially large optimization problems. This tool allows users to describe their problems with an intuitive model that is automatically transformed into a form handled by the large-scale solver, liberating users from performing tedious manual transformations. For the large-scale solver, we use the alternating direction method of multipliers (ADMM) and express conic optimization problems in consensus form, splitting the linear algebra from the generalized conic inequalities. For modeling optimization problems, we present the quadratic cone modeling language (QCML), which like CVX is a tool that automatically converts convex optimization problems into conic form and solves them with a standard cone solver. Unlike CVX, QCML can be used to analyze and generate code for entire problem families without requiring another analysis or generation phase when problem (instance) data or dimensions change.
Author: Dimitri Bertsekas Publisher: Athena Scientific ISBN: 1886529310 Category : Mathematics Languages : en Pages : 256
Book Description
An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).
Author: James Renegar Publisher: SIAM ISBN: 9780898718812 Category : Mathematics Languages : en Pages : 124
Book Description
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Author: Jacob Elliot Mattingley
Author: Jacob Elliot Mattingley
Author: Jacob Elliot Mattingley
Author: Peter Marwedel
Author: Aharon Ben-Tal
Author: Li Li
Author: Yurii Nesterov
Author: Rainer Leupers
Author: Eric Chu
Author: Dimitri Bertsekas
Author: James Renegar