Trust Region Methods

DOWNLOAD

Download Trust Region Methods PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Trust Region Methods book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Trust Region Methods

DOWNLOAD
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 For Unconstrained Optimization Problems

DOWNLOAD
Author : Mostafa Rezapour
language : en
Publisher:
Release Date : 2020

Trust Region Methods For Unconstrained Optimization Problems written by Mostafa Rezapour and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematical optimization categories.

We present trust-region methods for the general unconstrained minimization problem. Trust-region algorithms iteratively minimize a model of the objective function within the trust-region and update the size of the region to find a first-order stationary point for the objective function. The radius of the trust-region is updated based on the agreement between the model and the objective function at the new trial point. The efficiency of the trust-region algorithms depends significantly on the size of the trust-region, the agreement between the model and the objective function and the model value reduction at each step. The size of the trust-region at each step plays a key role in the efficiency of the trust-region algorithm, particularly for large scale problems, because constructing and minimizing the model at each step requires gradient and Hessian information of the objective function. If the trust-region is too small or too large, then more models must be constructed and minimized, which is computationally expensive. ‌We propose two adaptive trust-region algorithms that explore beyond the trust region if the boundary of the region prevents the algorithm from accepting a more beneficial point. It occurs when there is very good agreement between the model and the objective function on the trust-region boundary and we can find a step outside the trust-region with smaller model value while maintaining good agreement between the model and the objective function. We also take a different approach to derivative-free unconstrained optimization problems, where the objective function is possibly nonsmooth. We do an exploratory study by using deep neural-networks and their well-known capability as universal function approximator. We propose and investigate two derivative-free trust-region methods for solving unconstrained minimization problems, where we employ artificial neural-networks to construct a model within the trust-region. We directly find an estimate of the objective function minimizer without explicitly constructing a model function through a parent-child neural-network. This approach may provide improved practical performance in cases where the objective function is extremely noisy or stochastic. We provide a framework for future work in this area.

Large Scale Trust Region Methods And Their Application To Primal Dual Interior Point Methods

DOWNLOAD
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.

Iterative Methods For Optimization

DOWNLOAD
Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 1999-01-01

Iterative Methods For Optimization written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.

a carefully selected group of methods for unconstrained and bound constrained optimization problems is analyzed in depth both theoretically and algorithmically. The book focuses on clarity in algorithmic description and analysis rather than generality, and also provides pointers to the literature for the most general theoretical results and robust software,

Implementation Of Trust Region Methods In Optimization

DOWNLOAD
Author : Mohammed Omar Hajj
language : en
Publisher:
Release Date : 1998

Implementation Of Trust Region Methods In Optimization written by Mohammed Omar Hajj and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Dissertations, Academic categories.

Numerical Methods For Chemical Engineering

DOWNLOAD
Author : Kenneth J. Beers
language : en
Publisher: Cambridge University Press
Release Date : 2007

Numerical Methods For Chemical Engineering written by Kenneth J. Beers 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 2007 with Computers categories.

Applications of numerical mathematics and scientific computing to chemical engineering.

100 Optimization Techniques

DOWNLOAD
Author : Subrata Pandey
language : en
Publisher: SUBRATA PANDEY
Release Date : 2023-02-23

100 Optimization Techniques written by Subrata Pandey and has been published by SUBRATA PANDEY this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-23 with Technology & Engineering categories.

100 optimization techniques is intended as a handbook for optimization techniques. Optimization techniques and algorithms are methods used to find the most efficient solution to a problem. Different techniques and algorithms may be used to solve a particular problem, depending on the nature of the problem. Researchers from varieties of domains are using optimization algorithms to solve problems in their domain. Different optimization techniques have their pros and cons. This book serves as a handbook for researchers who wants to know about different optimization methods currently available and their operating principles. One hundred optimization techniques are arranged in an alphabetical order. Researchers and students who want to use different optimization techniques for solving their domain related problems will find this book helpful.

Engineering Design Optimization

DOWNLOAD
Author : Joaquim R. R. A. Martins
language : en
Publisher: Cambridge University Press
Release Date : 2021-11-18

Engineering Design Optimization written by Joaquim R. R. A. Martins 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 2021-11-18 with Mathematics categories.

A rigorous yet accessible graduate textbook covering both fundamental and advanced optimization theory and algorithms.

Trust Region Methods For Minimization

DOWNLOAD
Author : R. B. Schnabel
language : en
Publisher:
Release Date : 1984

Trust Region Methods For Minimization written by R. B. Schnabel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.

This research project investigated a number of topics in unconstrained optimization, constrained optimization, and solving systems of nonlinear equations. The biggest accomplishment was the development of a new class of of methods, called tensor methods, for solving systems of nonlinear equations. These methods led to large increases in efficiency over standard methods on extensive batteries of test problems, with especially large gains on problems with singular Jacobians at the solution. The other major accomplishment was the development of a unified theory of trust region methods for unconstrained optimization. Our theory shows how line search, dogleg, or optimal step methods can be constructed that satisfy first and second order conditions for convergence. Research was also completed on conic methods for optimization, on secant methods that satisfy multiple secant equations, and on issues concerned with the computation of null space bases in constrained optimization. Research was initiated on computational methods for nonlinear least squares problems with errors in the independent variables, and in parallel algorithms for optimization.

Recent Developments In Algorithms And Software For Trust Region Methods

DOWNLOAD
Author : Argonne National Laboratory. Mathematics and Computer Science Division
language : en
Publisher:
Release Date : 1982

Recent Developments In Algorithms And Software For Trust Region Methods written by Argonne National Laboratory. Mathematics and Computer Science Division and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.