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A Sequential Quadratic Programming Algorithm For Solving Large Sparse Nonlinear Programs
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Book Synopsis A Sequential Quadratic Programming Algorithm for Solving Large, Sparse Nonlinear Programs by : Ronald Harlan Nickel
Download or read book A Sequential Quadratic Programming Algorithm for Solving Large, Sparse Nonlinear Programs written by Ronald Harlan Nickel and published by . This book was released on 1984 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document describes the structure and theory for a sequential quadratic programming algorithm for solving large, sparse nonlinear optimization problems. Also provided are the details of a computer implementation of the algorithm, along with test results. The algorithm is based on Han's sequential quadratic programming method. It maintains a sparse approximation to the Cholesky factor of the Hessian of the Lagrangian and stores all gradients in a sparse format. The solution to the quadratic program generated at each step is obtained by solving the dual quadratic program using a projected conjugate gradient algorithm. Sine only active constraints are considered in forming the dual, the dual problem will normally be much smaller than the primal quadratic program and, hence, much easier to solve. An updating procedure is employed that does not destroy sparsity. Several test problems, ranging in size from 5 to 60 variables were solved with the algorithm. These results indicate that the algorithm has the potential to solve large, sparse nonlinear programs. The algorithm is especially attractive for solving problems having nonlinear constraints. (Author).
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 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Quadratic Programming Algorithms by : Zdenek Dostál
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.
Book Synopsis Large-scale Sequential Quadratic Programming Algorithms by :
Download or read book Large-scale Sequential Quadratic Programming Algorithms written by and published by . This book was released on 1992 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test 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:
Download or read book ICIAM 91 written by Robert E. O'Malley and published by SIAM. This book was released on 1992-01-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Computer Arithmetic, Algebra, OOP.
Author :Stanford University. Department of Operations Research. Systems Optimization Laboratory Publisher : ISBN 13 : Total Pages :98 pages Book Rating :4.F/5 ( download)
Book Synopsis Large-scale Sequential Quadratic Programming Algorithms by : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Download or read book Large-scale Sequential Quadratic Programming Algorithms written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1992 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Quadratic Programming Algorithms by : Zdenek Dostál
Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer. This book was released on 2008-11-01 with total page 0 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.
Book Synopsis High Performance Algorithms and Software in Nonlinear Optimization by : Renato de Leone
Download or read book High Performance Algorithms and Software in Nonlinear Optimization written by Renato de Leone and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years.
Book Synopsis Numerical Optimization 1984 by : Paul T. Boggs
Download or read book Numerical Optimization 1984 written by Paul T. Boggs and published by SIAM. This book was released on 1985-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solving Large Sparse Quadratic Programs with Simple Bounds by : Laurie Ann Hulbert
Download or read book Solving Large Sparse Quadratic Programs with Simple Bounds written by Laurie Ann Hulbert and published by . This book was released on 1990 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Method of Response Function in Psychology & Sociology by : Irina G. Malkina-Pykh
Download or read book The Method of Response Function in Psychology & Sociology written by Irina G. Malkina-Pykh and published by WIT Press. This book was released on 2013 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Social (psychological and sociological) systems present considerable difficulties for modellers due to their complexity, multidimensionality, uncertainty and irreducibility. The book proposes that response functions (MRF) be used as a method of constructing purposeful, credible and integrated social systems' models from data and prior knowledge or information. A semi-empirical, or "grey-box", MRF model may be regarded as a trade-off between a knowledge-based model and a "black-box" (empirical) model. It may embody all the existing knowledge on the process (or a part thereof) and, in addition, it relies on parameterised functions, whose parameters are determined from measurements. Observations contain hidden information on the processes under consideration and one of the main purposes of the proposed method is to "extract" and describe these hidden relationships. Parameterisation offers ways to couple qualitative with quantitative analysis. This combination makes it possible to take into account all the phenomena that are not modelled with the required accuracy through prior knowledge. Although only a simplified picture of the processes is modelled, a "grey box" system model provides some insight into the system processes. These processes are featured by chains of causality, highlighting stressors and variables responsive to stressors. The method of response functions is a nonlinear regression method that implies credible models in the sense that they are identifiable and, hopefully, explain system output behaviour satisfactorily. For case studies the authors have selected the problems usually studied by psychologists and sociologists with statistical procedures, such as investigation of variance and discriminant analysis based on the general linear model or one of its multivariate generalisations (structural equation models, etc.); disordered eating and obesity; subjective well-being and alexithymia. An accompanying CD-ROM contains the demonstration versions of three models that are discussed in the various chapters.The Method of Response Functions in Psychology and Sociology is aimed at Mathematical Psychologists; Mathematical Sociologists; Applied Psychologists; Sociologists and Social Practitioners. It will also be suitable for use on undergraduate as well as graduate and postgraduate courses specializing in these areas.
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 Algorithms for Nonlinear Programming by : Donald Goldfarb
Download or read book Algorithms for Nonlinear Programming written by Donald Goldfarb and published by . This book was released on 1985 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several algorithms for solving problems in linear, quadratic, and nonlinear programming, network flows, and facilities location were developed and analyzed. Results include: (1) The analysis of the computational complexity of the problem of determining an optimally sparse representation of the null space of a matrix, and the development of worst-case bounds for the shadow-vertex simplex algorithm and several heuristics for distance constrained discrete facility location problems and conditional covering problems; (2) The development of efficient algorithms for dense and sparse assignment problems, strictly convex quadratic programming problems, and a nonlinear programming problem that arises when maximizing a correlation coefficient subject to linear constraints; and (3) The application of iterative methods to large sparse equality-constraind quadratic programs and the development of multiple constraint deletion strategies for active-set algorithms for linearly consrained nonlinear programming problems. (Author).
Book Synopsis A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem by :
Download or read book A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem written by and published by . This book was released on 1993 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.
Author :Christine Anderson Publisher :AIAA (American Institute of Aeronautics & Astronautics) ISBN 13 : Total Pages :664 pages Book Rating :4.3/5 (91 download)
Book Synopsis Aerospace Software Engineering by : Christine Anderson
Download or read book Aerospace Software Engineering written by Christine Anderson and published by AIAA (American Institute of Aeronautics & Astronautics). This book was released on 1991 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aerospace Software Engineering brings you the knowledge of some of the finest software engineers in the worldin a single volume. This text is an essential guide for the aerospace program manager who must deal with software as part of the overall system and a valuable update for the practicing software engineer.
