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Author: Yves Dominique Brise Publisher: Logos Verlag Berlin GmbH ISBN: 3832533664 Category : Computers Languages : en Pages : 232
Book Description
This PhD thesis was written at ETH Zurich, in Prof. Dr. Emo Welzl's research group, under the supervision of Dr. Bernd Garnter. It shows two theoretical results that are both related to quadratic programming. The first one concerns the abstract optimization framework of violator spaces and the randomized procedure called Clarkson's algorithm. In a nutshell, the algorithm randomly samples from a set of constraints, computes an optimal solution subject to these constraints, and then checks whether the ignored constraints violate the solution. If not, some form of re-sampling occurs. We present the algorithm in the easiest version that can still be analyzed successfully. The second contribution concerns quadratic programming more directly. It is well-known that a simplex-like procedure can be applied to quadratic programming. The main computational effort in this algorithm comes from solving a series of linear equation systems that change gradually. We develop the integral LU decomposition of matrices, which allows us to solve the equation systems efficiently and to exploit sparse inputs. Last but not least, a considerable portion of the work included in this thesis was devoted to implementing the integral LU decomposition in the framework of the existing quadratic programming solver in the Computational Geometry Algorithms Library (CGAL). In the last two chapters we describe our implementation and the experimental results we obtained.
Author: Yves Dominique Brise Publisher: Logos Verlag Berlin GmbH ISBN: 3832533664 Category : Computers Languages : en Pages : 232
Book Description
This PhD thesis was written at ETH Zurich, in Prof. Dr. Emo Welzl's research group, under the supervision of Dr. Bernd Garnter. It shows two theoretical results that are both related to quadratic programming. The first one concerns the abstract optimization framework of violator spaces and the randomized procedure called Clarkson's algorithm. In a nutshell, the algorithm randomly samples from a set of constraints, computes an optimal solution subject to these constraints, and then checks whether the ignored constraints violate the solution. If not, some form of re-sampling occurs. We present the algorithm in the easiest version that can still be analyzed successfully. The second contribution concerns quadratic programming more directly. It is well-known that a simplex-like procedure can be applied to quadratic programming. The main computational effort in this algorithm comes from solving a series of linear equation systems that change gradually. We develop the integral LU decomposition of matrices, which allows us to solve the equation systems efficiently and to exploit sparse inputs. Last but not least, a considerable portion of the work included in this thesis was devoted to implementing the integral LU decomposition in the framework of the existing quadratic programming solver in the Computational Geometry Algorithms Library (CGAL). In the last two chapters we describe our implementation and the experimental results we obtained.
Author: Zdenek Dostál Publisher: Springer Science & Business Media ISBN: 0387848061 Category : Mathematics Languages : en Pages : 293
Book Description
Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Author: Amit Bhaya Publisher: SIAM ISBN: 0898716020 Category : Mathematics Languages : en Pages : 291
Book Description
This book organizes the analysis and design of iterative numerical methods from a control perspective. A variety of applications are discussed, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems and integration and shooting methods for ordinary differential equations.
Author: Michael J. Best Publisher: CRC Press ISBN: 1351647202 Category : Business & Economics Languages : en Pages : 423
Book Description
Quadratic programming is a mathematical technique that allows for the optimization of a quadratic function in several variables. QP is a subset of Operations Research and is the next higher lever of sophistication than Linear Programming. It is a key mathematical tool in Portfolio Optimization and structural plasticity. This is useful in Civil Engineering as well as Statistics.
Author: Zdenek Dostál Publisher: Springer ISBN: 9780387571447 Category : Mathematics Languages : en Pages : 0
Book Description
Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Author: Stanford University. Systems Optimization Laboratory Publisher: ISBN: Category : Languages : en Pages : 80
Book Description
This report describes a single-phase quadratic programming method, an active-set method which solves a sequence of equality-constraint quadratic programs.
Author: Christian Constanda Publisher: Springer ISBN: 3030160777 Category : Mathematics Languages : en Pages : 478
Book Description
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
Author: Yves Dominique Brise
Author: Yves Dominique Brise
Author: Zdenek Dostál
Author: Amit Bhaya
Author: Michael J. Best
Author: Zdenek Dostál
Author: William S. Dorn
Author: Stanford University. Systems Optimization Laboratory
Author: 
Author: Christian Constanda
Author: Martin Peter Neuenhofen