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Large Scale Sequential Quadratic Programming Algorithms
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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 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 Application of Sequential Quadratic Programming to Large-Scale Structural Design Problems by :
Download or read book Application of Sequential Quadratic Programming to Large-Scale Structural Design Problems written by and published by . This book was released on 1994 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale structural optimization problems are often difficult to solve with reasonable efficiency and accuracy. Such problems are often characterized by constraint functions which are not explicitly defined. Constraint and gradient functions are usually expensive to evaluate. An optimization approach which uses the NLPQL sequential quadratic programming algorithm of Schittkowski, integrated with the Automated Structural Optimization System (ASTROS) is tested. The traditional solution approach involves the formulation and solution of an explicitly defined approximate problem during each iteration. This approach is replaced by a simpler approach in which the approximate problem is eliminated. In the simpler approach, each finite element analysis is followed by one iteration of the optimizer. To compensate for the cost of additional analyses incurred by the elimination of the approximate problem, a much more restrictive active set strategy is used. The approach is applied to three large structures problems, including one with constraints from multiple disciplines. Results and algorithm performance comparisons are given. Although not much computational efficiency is gained, the alternative approach gives accurate solutions. The largest of the three problems, which had 1527 design variables and 6124 constraints was solved with ASTROS for the first time using a direct method. The resulting design represents the lowest weight feasible design recorded to date. Optimization, Structural optimization, Nonlinear programming, Sequential quadratic programming, Active set strategies.
Book Synopsis Large-Scale Optimization with Applications by :
Download or read book Large-Scale Optimization with Applications written by and published by Springer Science & Business Media. This book was released on 1997 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The theory and implementation of a large scale successive quadratic programming algorithm by : Deepa Mahidhara
Download or read book The theory and implementation of a large scale successive quadratic programming algorithm written by Deepa Mahidhara and published by . This book was released on 1989 with total page 276 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 SQP Methods for Large-scale Optimization by : Alexander Barclay
Download or read book SQP Methods for Large-scale Optimization written by Alexander Barclay and published by . This book was released on 1999 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Large-scale Numerical Optimization by : Thomas Frederick Coleman
Download or read book Large-scale Numerical Optimization written by Thomas Frederick Coleman and published by SIAM. This book was released on 1990-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.
Book Synopsis An algorithm for large scale quadratic programming by : Nicholas I M. Gould
Download or read book An algorithm for large scale quadratic programming written by Nicholas I M. Gould and published by . This book was released on 1989 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Sequential Quadratic Programming Algorithms for Optimization by : Francisco Javier Prieto
Download or read book Sequential Quadratic Programming Algorithms for Optimization written by Francisco Javier Prieto and published by . This book was released on 1989 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology by : Neculai Andrei
Download or read book Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology written by Neculai Andrei and published by Springer. This book was released on 2017-12-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.
Book Synopsis Large-Scale PDE-Constrained Optimization by : Lorenz T. Biegler
Download or read book Large-Scale PDE-Constrained Optimization written by Lorenz T. Biegler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.
Download or read book Very large scale optimization written by and published by DIANE Publishing. This book was released on with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algorithms for Continuous Optimization by : E. Spedicato
Download or read book Algorithms for Continuous Optimization written by E. Spedicato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.
Book Synopsis An Algorithm for Large-scale Quadratic Programming Problems and Its Extensions to the Linearly Constrained Nonlinear Case by : L. F. Escudero
Download or read book An Algorithm for Large-scale Quadratic Programming Problems and Its Extensions to the Linearly Constrained Nonlinear Case written by L. F. Escudero and published by . This book was released on 1981 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Algorithm for Structured, Large-Scale Quadratic Programming Problems by : Cu Duong Ha
Download or read book An Algorithm for Structured, Large-Scale Quadratic Programming Problems written by Cu Duong Ha and published by . This book was released on 1981 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: An algorithm for structured, large-scale, convex quadratic programming problems is described. The structure of the constraint matrix is block diagonal with a small number of coupling constraints and variables. The algorithm utilizes twice a decomposition procedure that was developed earlier. The first time the decomposition procedure is used to break up the coupling constraints, and the second time it is used to break up the coupling variables. Preliminary computational results are also reported. The block diagonal structure with a small number of coupling constraints and variables usually arises from the formulation of multitime period and multidivision production scheduling and distribution models in large corporations. Each block is concerned with the operation of one division during one time period considered in isolation. The coupling constraints arise from the use of common resources of all divisions or from combining the output of divisions to meet overall demands. The coupling variables represent activities that affect the operation of divisions in more than one time period.
