Trust Region Methods For Minimization

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Trust Region Methods For Minimization

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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.

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 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.

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.

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.

Mathematical Programming The State Of The Art

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Author : A. Bachem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematical Programming The State Of The Art written by A. Bachem 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 2012-12-06 with Mathematics categories.

In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.

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.

On Trust Region Methods For Unconstrained Minimization Without Derivatives

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Author : M. J. D. Powell
language : en
Publisher:
Release Date : 2002

On Trust Region Methods For Unconstrained Minimization Without Derivatives written by M. J. D. Powell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

A Trust Region Framework For Managing The Use Of Approximation Models In Optimization

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Author : Institute for Computer Applications in Science and Engineering
language : en
Publisher:
Release Date : 1997

A Trust Region Framework For Managing The Use Of Approximation Models In Optimization written by Institute for Computer Applications in Science and Engineering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

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.