A Recursive Trust Region Method For Non Convex Constrained Minimization
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A Recursive Trust Region Method For Non Convex Constrained Minimization
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Author : Christian Groß
language : en
Publisher:
Release Date : 2008
A Recursive Trust Region Method For Non Convex Constrained Minimization written by Christian Groß and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Trust Region Methods
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Author : A. R. Conn
language : en
Publisher: SIAM
Release Date : 2000-01-01
Trust Region Methods written by A. R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization.
Trust Region Methods
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Author : A. R. Conn
language : en
Publisher: SIAM
Release Date : 2000-01-01
Trust Region Methods written by A. R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Mathematics of Computing -- General.
Domain Decomposition Methods In Science And Engineering Xviii
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Author : Michel Bercovier
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-01
Domain Decomposition Methods In Science And Engineering Xviii written by Michel Bercovier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with Mathematics categories.
th This volume contains a selection of 41 refereed papers presented at the 18 International Conference of Domain Decomposition Methods hosted by the School of ComputerScience and Engineering(CSE) of the Hebrew Universityof Jerusalem, Israel, January 12–17, 2008. 1 Background of the Conference Series The International Conference on Domain Decomposition Methods has been held in twelve countries throughout Asia, Europe, the Middle East, and North America, beginning in Paris in 1987. Originally held annually, it is now spaced at roughly 18-month intervals. A complete list of past meetings appears below. The principal technical content of the conference has always been mathematical, but the principal motivation has been to make ef cient use of distributed memory computers for complex applications arising in science and engineering. The leading 15 such computers, at the “petascale” characterized by 10 oating point operations per second of processing power and as many Bytes of application-addressablem- ory, now marshal more than 200,000 independentprocessor cores, and systems with many millions of cores are expected soon. There is essentially no alternative to - main decomposition as a stratagem for parallelization at such scales. Contributions from mathematicians, computerscientists, engineers,and scientists are together n- essary in addressing the challenge of scale, and all are important to this conference.
Large Scale Trust Region Methods And Their Application To Primal Dual Interior Point Methods
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Author : Alexander Guldemond
language : en
Publisher:
Release Date : 2023
Large Scale Trust Region Methods And Their Application To Primal Dual Interior Point Methods written by Alexander Guldemond and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Trust-region methods are amongst the most commonly used methods in unconstrained mathematical optimization. Their impressive performance and sound theoretical guarantees make them suitable for a wide range of problem types. However, the computational complexity of existing methods for solving the trust-region subproblem prevents trust-region methods from being widely used in large-scale problems in both unconstrained and constrained settings. This dissertation introduces and analyzes three novel methods for solving the trust-region subproblem for large-scale constrained optimization problems. Convergence rates and proofs are presented where applicable. Furthermore, a trust-region approach is developed for the recently introduced all-shifted primal-dual penalty-barrier method for solving nonconvex, constrained optimization problems. The three trust-region algorithms introduced are the shifted and inverted generalized Lanczos trust region algorithm, the locally optimal preconditioned conjugate gradient trust region, and the Jacobi-Davidson QZ trust region algorithm. Each new method exhibits improved performance over the existing standard methods and is best suited for problems too large for the traditional methods to handle efficiently. Furthermore, each method exhibits particular benefits for differently scaled problems.
Structured Trust Region Algorithms For The Minimization Of Nonlinear Functions
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Author : Johara Shireen Shahabuddin
language : en
Publisher:
Release Date : 1996
Structured Trust Region Algorithms For The Minimization Of Nonlinear Functions written by Johara Shireen Shahabuddin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Primal Dual Trust Region Methods For Nonlinear Programming
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Author : Yesheng Huang
language : en
Publisher:
Release Date : 2023
Primal Dual Trust Region Methods For Nonlinear Programming written by Yesheng Huang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
The goal of this dissertation is to investigate the formulation and analysis of a trust-region interior-point method for solving nonconvex optimization problems with a mixture of equality and inequality constraints. The proposed method is based on minimizing a merit function that may be interpreted as a shifted primal-dual penalty-barrier function. The method generates a sequence of iterates with limit points that are either infeasible stationary points or complementary approximate Karush-Kuhn-Tucker points, i.e., every limit point satisfies reasonable stopping criteria and is a Karush-Kuhn-Tucker point under a regularity condition that is the weakest constraint qualification associated with sequential optimality conditions. Under suitable additional assumptions, the method is equivalent to a shifted variant of the primal-dual path-following method in the neighborhood of a solution.The proposed method has an inner/outer iteration structure. The outer iteration specifies the form of the merit function. The inner iteration optimizes the merit function with fixed parameters using a trust-region method. The algorithm for solving the trust-region subproblem involves a procedure based on the application of a one-dimensional Newton's method. Methods are proposed for treating the so-called "hard case" in which no root of the one dimensional equation exists.
Domain Decomposition Methods In Science And Engineering Xxvi
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Author : Susanne C. Brenner
language : en
Publisher: Springer Nature
Release Date : 2023-03-15
Domain Decomposition Methods In Science And Engineering Xxvi written by Susanne C. Brenner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Mathematics categories.
These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Introduction To Derivative Free Optimization
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Author : Andrew R. Conn
language : en
Publisher: SIAM
Release Date : 2009-04-16
Introduction To Derivative Free Optimization written by Andrew R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-16 with Mathematics categories.
The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.