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Author :
Publisher : Stanford University
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4./5 ( download)
Download or read book A Regularized Active-Set method For Sparse Convex Quadratic Programming written by and published by Stanford University. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 686 pages
Book Rating : 4.3/5 (874 download)
Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Author : Stanford University. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 80 pages
Book Rating : 4.F/5 ( download)
Download or read book A Single-phase Method for Quadratic Programming written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1986 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report describes a single-phase quadratic programming method, an active-set method which solves a sequence of equality-constraint quadratic programs.
Author : Elizabeth Lai Sum Wong
Publisher :
ISBN 13 : 9781124691152
Total Pages : 125 pages
Book Rating : 4.6/5 (911 download)
Download or read book Active-set Methods for Quadratic Programming written by Elizabeth Lai Sum Wong and published by . This book was released on 2011 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational methods are considered for finding a point satisfying the second-order necessary conditions for a general (possibly nonconvex) quadratic program (QP). A framework for the formulation and analysis of feasible-point active-set methods is proposed for a generic QP. This framework is defined by reformulating and extending an inertia-controlling method for general QP that was first proposed by Fletcher and subsequently modified by Gould. This reformulation defines a class of methods in which a primal-dual search pair is the solution of a "KKT system'' of equations associated with an equality-constrained QP subproblem defined in terms of a "working set'' of linearly independent constraints. It is shown that, under certain circumstances, the solution of this KKT system may be updated using a simple recurrence relation, thereby giving a significant reduction in the number of systems that need to be solved. The use of inertia control guarantees that the KKT systems remain nonsingular throughout, thereby allowing the utilization of third-party linear algebra software. The algorithm is suitable for indefinite problems, making it an ideal QP solver for stand-alone applications and for use within a sequential quadratic programming method using exact second derivatives. The proposed framework is applied to primal and dual quadratic problems, as well as to single-phase problems that combine the feasibility and optimality phases of the active-set method, producing a range of formats that are suitable for a variety of applications. The algorithm is implemented in the Fortran code icQP. Its performance is evaluated using different symmetric and unsymmetric linear solvers on a set of convex and nonconvex problems. Results are presented that compare the performance of icQP with the convex QP solver SQOPT on a large set of convex problems.
Author : Herbert Fischer
Publisher : Springer Science & Business Media
ISBN 13 : 3642997899
Total Pages : 371 pages
Book Rating : 4.6/5 (429 download)
Download or read book Applied Mathematics and Parallel Computing written by Herbert Fischer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors of this Festschrift prepared these papers to honour and express their friendship to Klaus Ritter on the occasion of his sixtieth birthday. Be cause of Ritter's many friends and his international reputation among math ematicians, finding contributors was easy. In fact, constraints on the size of the book required us to limit the number of papers. Klaus Ritter has done important work in a variety of areas, especially in var ious applications of linear and nonlinear optimization and also in connection with statistics and parallel computing. For the latter we have to mention Rit ter's development of transputer workstation hardware. The wide scope of his research is reflected by the breadth of the contributions in this Festschrift. After several years of scientific research in the U.S., Klaus Ritter was ap pointed as full professor at the University of Stuttgart. Since then, his name has become inextricably connected with the regularly scheduled conferences on optimization in Oberwolfach. In 1981 he became full professor of Applied Mathematics and Mathematical Statistics at the Technical University of Mu nich. In addition to his university teaching duties, he has made the activity of applying mathematical methods to problems of industry to be centrally important.
Author : Daniel Arnström
Publisher : Linköping University Electronic Press
ISBN 13 : 9179296920
Total Pages : 45 pages
Book Rating : 4.1/5 (792 download)
Download or read book On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC written by Daniel Arnström and published by Linköping University Electronic Press. This book was released on 2021-03-03 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations is solved. The primary contribution of this thesis is a method which determines which sequence of subproblems a popular class of such active-set algorithms need to solve, for every possible QP instance that might arise from a given linear MPC problem (i.e, for every possible state and reference signal). By knowing these sequences, worst-case bounds on how many iterations, floating-point operations and, ultimately, the maximum solution time, these active-set algorithms require to compute a solution can be determined, which is of importance when, e.g, linear MPC is used in safety-critical applications. After establishing this complexity certification method, its applicability is extended by showing how it can be used indirectly to certify the complexity of another, efficient, type of active-set QP algorithm which reformulates the QP as a nonnegative least-squares method. Finally, the proposed complexity certification method is extended further to situations when enhancements to the active-set algorithms are used, namely, when they are terminated early (to save computations) and when outer proximal-point iterations are performed (to improve numerical stability).
Author : Zdenek Dostál
Publisher : Springer Science & Business Media
ISBN 13 : 0387848061
Total Pages : 293 pages
Book Rating : 4.3/5 (878 download)
Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Christopher Mario Maes
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (688 download)
Download or read book A Regularized Active-set Method for Sparse Convex Quadratic Programming written by Christopher Mario Maes and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An active-set algorithm is developed for solving convex quadratic programs (QPs). The algorithm employs primal regularization within a bound-constrained augmented Lagrangian method. This leads to a sequence of QP subproblems that are feasible and strictly convex, and whose KKT systems are guaranteed to be nonsingular for any active set. A simplified, single-phase algorithm becomes possible for each QP subproblem. There is no need to control the inertia of the KKT system defining each search direction, and a simple step-length procedure may be used without risk of cycling in the presence of degeneracy. Since all KKT systems are nonsingular, they can be factored with a variety of sparse direct linear solvers. Block-LU updates of the KKT factors allow for active-set changes. The principal benefit of primal and dual regularization is that warm starts are possible from any given active set. This is vital inside sequential quadratic programming (SQP) methods for nonlinear optimization, such as the SNOPT solver. The method provides a reliable approach to solving sparse generalized least-squares problems. Ordinary least-squares problems with Tikhonov regularization and bounds can be solved as a single QP subproblem. The algorithm is implemented as the QPBLUR solver (Matlab and Fortran 95 versions) and the Fortran version has been integrated into SNOPT. The performance of QPBLUR is evaluated on a test set of large convex QPs, and on the sequences of QPs arising from SNOPT's SQP method.
Author : Wayne Durham
Publisher : John Wiley & Sons
ISBN 13 : 1118827791
Total Pages : 308 pages
Book Rating : 4.1/5 (188 download)
Download or read book Aircraft Control Allocation written by Wayne Durham and published by John Wiley & Sons. This book was released on 2017-01-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aircraft Control Allocation Wayne Durham, Virginia Polytechnic Institute and State University, USA Kenneth A. Bordignon, Embry-Riddle Aeronautical University, USA Roger Beck, Dynamic Concepts, Inc., USA An authoritative work on aircraft control allocation by its pioneers Aircraft Control Allocation addresses the problem of allocating supposed redundant flight controls. It provides introductory material on flight dynamics and control to provide the context, and then describes in detail the geometry of the problem. The book includes a large section on solution methods, including 'Banks' method', a previously unpublished procedure. Generalized inverses are also discussed at length. There is an introductory section on linear programming solutions, as well as an extensive and comprehensive appendix dedicated to linear programming formulations and solutions. Discrete-time, or frame-wise allocation, is presented, including rate-limiting, nonlinear data, and preferred solutions. Key features: Written by pioneers in the field of control allocation. Comprehensive explanation and discussion of the major control allocation solution methods. Extensive treatment of linear programming solutions to control allocation. A companion web site contains the code of a MATLAB/Simulink flight simulation with modules that incorporate all of the major solution methods. Includes examples based on actual aircraft. The book is a vital reference for researchers and practitioners working in aircraft control, as well as graduate students in aerospace engineering.
Author : Michael J. Best
Publisher : CRC Press
ISBN 13 : 1351647202
Total Pages : 423 pages
Book Rating : 4.3/5 (516 download)
Download or read book Quadratic Programming with Computer Programs written by Michael J. Best and published by CRC Press. This book was released on 2017-07-12 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ekaterina A. Kostina
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (767 download)
Download or read book A Primal-dual Active-set Method for Convex Quadratic Programming written by Ekaterina A. Kostina and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yurii Nesterov
Publisher : SIAM
ISBN 13 : 9781611970791
Total Pages : 414 pages
Book Rating : 4.9/5 (77 download)
Download or read book Interior-point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Katta G. Murty
Publisher :
ISBN 13 :
Total Pages : 604 pages
Book Rating : 4.3/5 (91 download)
Download or read book Linear and Combinatorial Programming written by Katta G. Murty and published by . This book was released on 1985 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Claude Lemarechal
Publisher : Elsevier
ISBN 13 : 1483188760
Total Pages : 195 pages
Book Rating : 4.4/5 (831 download)
Download or read book Nonsmooth Optimization written by Claude Lemarechal and published by Elsevier. This book was released on 2014-05-19 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth Optimization contains the proceedings of a workshop on non-smooth optimization (NSO) held from March 28 to April 8,1977 in Austria under the auspices of the International Institute for Applied Systems Analysis. The papers explore the techniques and theory of NSO and cover topics ranging from systems of inequalities to smooth approximation of non-smooth functions, as well as quadratic programming and line searches. Comprised of nine chapters, this volume begins with a survey of Soviet research on subgradient optimization carried out since 1962, followed by a discussion on rates of convergence in subgradient optimization. The reader is then introduced to the method of subgradient optimization in an abstract setting and the minimal hypotheses required to ensure convergence; NSO and nonlinear programming; and bundle methods in NSO. A feasible descent algorithm for linearly constrained least squares problems is described. The book also considers sufficient minimization of piecewise-linear univariate functions before concluding with a description of the method of parametric decomposition in mathematical programming. This monograph will be of interest to mathematicians and mathematics students.
Author : Gergely Takács
Publisher : Springer Science & Business Media
ISBN 13 : 1447123328
Total Pages : 535 pages
Book Rating : 4.4/5 (471 download)
Download or read book Model Predictive Vibration Control written by Gergely Takács and published by Springer Science & Business Media. This book was released on 2012-03-14 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-time model predictive controller (MPC) implementation in active vibration control (AVC) is often rendered difficult by fast sampling speeds and extensive actuator-deformation asymmetry. If the control of lightly damped mechanical structures is assumed, the region of attraction containing the set of allowable initial conditions requires a large prediction horizon, making the already computationally demanding on-line process even more complex. Model Predictive Vibration Control provides insight into the predictive control of lightly damped vibrating structures by exploring computationally efficient algorithms which are capable of low frequency vibration control with guaranteed stability and constraint feasibility. In addition to a theoretical primer on active vibration damping and model predictive control, Model Predictive Vibration Control provides a guide through the necessary steps in understanding the founding ideas of predictive control applied in AVC such as: · the implementation of computationally efficient algorithms · control strategies in simulation and experiment and · typical hardware requirements for piezoceramics actuated smart structures. The use of a simple laboratory model and inclusion of over 170 illustrations provides readers with clear and methodical explanations, making Model Predictive Vibration Control the ideal support material for graduates, researchers and industrial practitioners with an interest in efficient predictive control to be utilized in active vibration attenuation.
Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.F/5 ( download)
Download or read book Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1990 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard W. Cottle
Publisher : Springer
ISBN 13 : 1493970550
Total Pages : 644 pages
Book Rating : 4.4/5 (939 download)
Download or read book Linear and Nonlinear Optimization written by Richard W. Cottle and published by Springer. This book was released on 2017-06-11 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia
