Algorithms for Minimization Without Derivatives PDF Download
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Author: Richard P. Brent
Publisher: Courier Corporation
ISBN: 0486143686
Category : Mathematics
Languages : en
Pages : 210
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Book Description
DIVOutstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. /div
Author: Richard P. Brent
Publisher: Courier Corporation
ISBN: 0486143686
Category : Mathematics
Languages : en
Pages : 210
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Book Description
DIVOutstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. /div
Author: Richard P. Brent
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 656
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Book Description
Theorems are given concerning the order (i.e., rate) of convergence of a successive interpolation process for finding simple zeros of a function or its derivatives, using only function evaluations. Special cases include the successive linear interpolation process for finding zeros, and a parabolic interpolation process for finding turning points. Results on interpolation and finite differences include weakening the hypotheses of a theorem of Ralston on the derivative of the error in Lagrangian interpolation. The theoretical results are applied to given algorithms for finding zeros or local minima of functions of one variable, in the presence of rounding errors. The algorithms are guaranteed to converge nearly as fast as would bisection or Fibonacci search, and in most practical cases convergence is superlinear, and much faster than for bisection or Fibonacci search. (Author).
Author: S. Gomez
Publisher: Springer Science & Business Media
ISBN: 9401583307
Category : Mathematics
Languages : en
Pages : 285
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Book Description
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.
Author: Gianni Pillo
Publisher: Springer Science & Business Media
ISBN: 0387300651
Category : Mathematics
Languages : en
Pages : 297
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Book Description
This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
Author: C. T. Kelley
Publisher: SIAM
ISBN: 1611971896
Category : Mathematics
Languages : en
Pages : 171
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Book Description
A description of the implicit filtering algorithm, its convergence theory and a new MATLAB® implementation.
Author: Mykel J. Kochenderfer
Publisher: MIT Press
ISBN: 0262039427
Category : Computers
Languages : en
Pages : 521
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Book Description
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.
Author: Albert G. Holzman
Publisher: CRC Press
ISBN: 100014612X
Category : Computers
Languages : en
Pages : 393
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Book Description
This book covers the fundamentals of linear programming, extension of linear programming to discrete optimization methods, multi-objective functions, quadratic programming, geometric programming, and classical calculus methods for solving nonlinear programming problems.
Author: William H. Press
Publisher: Cambridge University Press
ISBN: 0521880688
Category : Computers
Languages : en
Pages : 1195
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Book Description
Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in colour for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support, or to subscribe to an online version, please visit www.nr.com.
Author: R. Fletcher
Publisher: John Wiley & Sons
ISBN: 111872318X
Category : Mathematics
Languages : en
Pages : 470
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Book Description
Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.
Author: Andrew R. Conn
Publisher: SIAM
ISBN: 0898716683
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
