Author: Stanford University. Department of Operations Research. Systems Optimization LaboratoryPublisher:
ISBN:
Category :
Languages : en
Pages : 18
Book Description
Cholesky-based Methods for Sparse Least Squares: the Benefits of Regularization
Author: Stanford University. Department of Operations Research. Systems Optimization LaboratoryPublisher:
ISBN:
Category :
Languages : en
Pages : 18
Book Description
Linear and Nonlinear Conjugate Gradient-related Methods
Author: Loyce M. AdamsPublisher: SIAM
ISBN: 9780898713763
Category : Mathematics
Languages : en
Pages : 186
Book Description
Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.
Algorithms for Sparse Linear Systems
Author: Jennifer ScottPublisher: Springer Nature
ISBN: 3031258207
Category : Mathematics
Languages : en
Pages : 254
Book Description
Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.
Solution of Sparse Linear Equations Using Cholesky Factors of Augmented Systems
Author: Michael A. SaundersCode Generation for Embedded Convex Optimization
Author: Jacob Elliot MattingleyPublisher: 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.
Applied Mechanics Reviews
Author: BIT.
Author: Stable Reduction to KKT Systems in Barrier Methods for Linear and Quadratic Programming
Author: Stanford University. Engineering-Economic Systems and Operations Research Department. Systems Optimization LaboratoryPublisher:
ISBN:
Category : Linear programming
Languages : en
Pages : 16
Book Description
Abstract: "We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2 X 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justify symmetrizing the KKT systems, we assume the use of a sparse solver whose numerical properties are independent of row and column scaling. In particular, we regularize the problem and use indefinite Cholesky-type factorizations. An implementation within OSL is tested on the larger NETLIB examples."
Super-Resolution for Remote Sensing
Author: Michal KawulokPublisher: Springer Nature
ISBN: 3031681061
Category :
Languages : en
Pages : 392
Book Description
Author: