Trust Region Methods

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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.

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.

Advances In Optimization And Numerical Analysis

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Author : S. Gomez
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Advances In Optimization And Numerical Analysis written by S. Gomez 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 2013-03-09 with Mathematics categories.

In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.

Trust Region Methods

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Author : Timothy Squires
language : en
Publisher:
Release Date : 2007

Trust Region Methods written by Timothy Squires and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Estimation theory categories.

Implementation Of Trust Region Methods In Optimization

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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.

Optimization In Chemical Engineering

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Author : Suman Dutta
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-11

Optimization In Chemical Engineering written by Suman Dutta 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 2016-03-11 with Technology & Engineering categories.

Optimization is used to determine the most appropriate value of variables under given conditions. The primary focus of using optimisation techniques is to measure the maximum or minimum value of a function depending on the circumstances. This book discusses problem formulation and problem solving with the help of algorithms such as secant method, quasi-Newton method, linear programming and dynamic programming. It also explains important chemical processes such as fluid flow systems, heat exchangers, chemical reactors and distillation systems using solved examples. The book begins by explaining the fundamental concepts followed by an elucidation of various modern techniques including trust-region methods, Levenberg–Marquardt algorithms, stochastic optimization, simulated annealing and statistical optimization. It studies the multi-objective optimization technique and its applications in chemical engineering and also discusses the theory and applications of various optimization software tools including LINGO, MATLAB, MINITAB and GAMS.

Trust Region Methods For Unconstrained Optimization Problems

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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.

Combination Trust Region Line Search Methods For Unconstrained Optimization

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Author : Edward Michael Gertz
language : en
Publisher:
Release Date : 1998

Combination Trust Region Line Search Methods For Unconstrained Optimization written by Edward Michael Gertz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Trust Region Methods For Simulation Based Nonlinear Optimization

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Author : Alexander Thekale
language : en
Publisher:
Release Date : 2011

Trust Region Methods For Simulation Based Nonlinear Optimization written by Alexander Thekale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.