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.

Iterative Methods For Optimization

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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.

This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

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.

Optimization Theory And Methods

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Author : Wenyu Sun
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-06

Optimization Theory And Methods written by Wenyu Sun 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 2006-08-06 with Mathematics categories.

Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.

100 Optimization Techniques

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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.

Numerical Methods For Chemical Engineering

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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.

Encyclopedia Of Optimization

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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04

Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Algorithms For Optimization

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Author : Mykel J. Kochenderfer
language : en
Publisher: MIT Press
Release Date : 2019-03-26

Algorithms For Optimization written by Mykel J. Kochenderfer and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-26 with Computers categories.

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

Newton Type Methods For Optimization And Variational Problems

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Author : Alexey F. Izmailov
language : en
Publisher: Springer
Release Date : 2014-07-08

Newton Type Methods For Optimization And Variational Problems written by Alexey F. Izmailov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Business & Economics categories.

This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Optimization Techniques And Applications With Examples

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Author : Xin-She Yang
language : en
Publisher: John Wiley & Sons
Release Date : 2018-09-19

Optimization Techniques And Applications With Examples written by Xin-She Yang and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-19 with Mathematics categories.

A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniques in optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The author—a noted expert in the field—covers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming. In addition, the book discusses artificial neural network, clustering and classifications, constraint-handling, queueing theory, support vector machine and multi-objective optimization, evolutionary computation, nature-inspired algorithms and many other topics. Designed as a practical resource, all topics are explained in detail with step-by-step examples to show how each method works. The book’s exercises test the acquired knowledge that can be potentially applied to real problem solving. By taking an informal approach to the subject, the author helps readers to rapidly acquire the basic knowledge in optimization, operational research, and applied data mining. This important resource: Offers an accessible and state-of-the-art introduction to the main optimization techniques Contains both traditional optimization techniques and the most current algorithms and swarm intelligence-based techniques Presents a balance of theory, algorithms, and implementation Includes more than 100 worked examples with step-by-step explanations Written for upper undergraduates and graduates in a standard course on optimization, operations research and data mining, Optimization Techniques and Applications with Examples is a highly accessible guide to understanding the fundamentals of all the commonly used techniques in optimization.