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Inertia Controlling Methods For Quadratic Programming
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Book Synopsis Inertia-controlling Methods for Quadratic Programming by : Philip E. Gill
Download or read book Inertia-controlling Methods for Quadratic Programming written by Philip E. Gill and published by . This book was released on 1988 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We also derive recurrance relations that facilitate the efficient implementation of a class of inertia-controlling methods that maintain the factorization of a nonsingular matrix associated with the Karush-Kuhn-Tucker conditions."
Author :Stanford University. Department of Operations Research. Systems Optimization Laboratory Publisher : ISBN 13 : Total Pages :30 pages Book Rating :4.F/5 ( download)
Book Synopsis On the Identification of Local Minimizers in Inertia-controlling Methods for Quadratic Programming by : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Download or read book On the Identification of Local Minimizers in Inertia-controlling Methods for Quadratic Programming written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1989 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Active-set Methods for Quadratic Programming by : Elizabeth Lai Sum Wong
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.
Book Synopsis A Regularized Active-Set method For Sparse Convex Quadratic Programming by :
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:
Book Synopsis Primal-Dual Interior Methods for Quadratic Programming by : Anna Shustrova
Download or read book Primal-Dual Interior Methods for Quadratic Programming written by Anna Shustrova and published by . This book was released on 2015 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted \barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of nonconvex problems. The second method is intended for problems with a mixture of equality and inequality constraints. In this case, the QP constraints are converted to so-called standard form and a primal-dual augmented Lagrangian is used to ensure the feasibility of the equality constraints in the limit.
Book Synopsis A Single-phase Method for Quadratic Programming by : Stanford University. Systems Optimization Laboratory
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.
Book Synopsis A Regularized Active-set Method for Sparse Convex Quadratic Programming by : Christopher Mario Maes
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.
Book Synopsis Optimal Control of ODEs and DAEs by : Matthias Gerdts
Download or read book Optimal Control of ODEs and DAEs written by Matthias Gerdts and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Optimization by : Jorge Nocedal
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.
Book Synopsis Computational Issues in High Performance Software for Nonlinear Optimization by : Almerico Murli
Download or read book Computational Issues in High Performance Software for Nonlinear Optimization written by Almerico Murli and published by Springer. This book was released on 2007-06-14 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Issues in High Performance Software for Nonlinear Research brings together in one place important contributions and up-to-date research results in this important area. Computational Issues in High Performance Software for Nonlinear Research serves as an excellent reference, providing insight into some of the most important research issues in the field.
Book Synopsis Technical Reports Awareness Circular : TRAC. by :
Download or read book Technical Reports Awareness Circular : TRAC. written by and published by . This book was released on 1989-11 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1990 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mixed Integer Nonlinear Programming by : Jon Lee
Download or read book Mixed Integer Nonlinear Programming written by Jon Lee and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
Book Synopsis Modern Numerical Nonlinear Optimization by : Neculai Andrei
Download or read book Modern Numerical Nonlinear Optimization written by Neculai Andrei and published by Springer Nature. This book was released on 2022-10-18 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.
Book Synopsis Integral Methods for Quadratic Programming by : Yves Dominique Brise
Download or read book Integral Methods for Quadratic Programming written by Yves Dominique Brise and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computational Intelligence in Optimization by : Yoel Tenne
Download or read book Computational Intelligence in Optimization written by Yoel Tenne and published by Springer Science & Business Media. This book was released on 2010-06-30 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of recent studies spans a range of computational intelligence applications, emphasizing their application to challenging real-world problems. Covers Intelligent agent-based algorithms, Hybrid intelligent systems, Machine learning and more.
