Book Chapter10.1016/B978-0-12-597050-1.50006-3
A New Algorithm for Unconstrained Optimization
M. J. D. Powell
- 01 Jan 1970
- pp 31-65
486
TL;DR: A new algorithm is described for calculating the least value of a given differentiable function of several variables that may be preferable to current algorithms for solving many unconstrained minimization problems.
read more
Abstract: A new algorithm is described for calculating the least value of a given differentiable function of several variables. The user must program the evaluation of the function and its first derivatives. Some convergence theorems are given that impose very mild conditions on the objective function. These theorems, together with some numerical results, indicate that the new method may be preferable to current algorithms for solving many unconstrained minimization problems.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
Pauli Virtanen,Ralf Gommers,Travis E. Oliphant,Matt Haberland,Matt Haberland,Tyler Reddy,David Cournapeau,Evgeni Burovski,Pearu Peterson,Warren Weckesser,Jonathan Bright,Stefan van der Walt,Matthew Brett,Joshua Wilson,K. Jarrod Millman,Nikolay Mayorov,Andrew Nelson,Eric Jones,Robert Kern,Eric B. Larson,CJ Carey,Ilhan Polat,Yu Feng,Eric Moore,Jake Vanderplas,Denis Laxalde,Josef Perktold,Robert Cimrman,Ian Henriksen,Ian Henriksen,E. A. Quintero,Charles R. Harris,Anne M. Archibald,Antônio H. Ribeiro,Fabian Pedregosa,Paul van Mulbregt,SciPy . Contributors +36 more
TL;DR: SciPy as discussed by the authors is an open source scientific computing library for the Python programming language, which includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics.
SciPy 1.0: fundamental algorithms for scientific computing in Python.
Pauli Virtanen,Ralf Gommers,Travis E. Oliphant,Matt Haberland,Matt Haberland,Tyler Reddy,David Cournapeau,Evgeni Burovski,Pearu Peterson,Warren Weckesser,Jonathan Bright,Stefan van der Walt,Matthew Brett,Joshua Wilson,K. Jarrod Millman,Nikolay Mayorov,Andrew Nelson,Eric Jones,Robert Kern,Eric B. Larson,CJ Carey,Ilhan Polat,Yu Feng,Eric Moore,Jake Vanderplas,Denis Laxalde,Josef Perktold,Robert Cimrman,Ian Henriksen,Ian Henriksen,E. A. Quintero,Charles R. Harris,Anne M. Archibald,Antônio H. Ribeiro,Fabian Pedregosa,Paul van Mulbregt,SciPy . Contributors +36 more
TL;DR: SciPy as discussed by the authors is an open-source scientific computing library for the Python programming language, which has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year.
Direct methods for sparse matrices
TL;DR: This book aims to be suitable also for a student course, probably at MSc level, and the subject is intensely practical and this book is written with practicalities ever in mind.
2K
Quasi-Newton Methods, Motivation and Theory
John E. Dennis,Jorge J. Moré +1 more
TL;DR: In this paper, an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton''s method for general and gradient nonlinear systems of equations is made, and references are given to ample numerical justification; here we give an overview of many of the important theoretical results.
Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming
TL;DR: A Generalized Reduced Gradient algorithm for nonlinear programming, its implementation as a FORTRAN program for solving small to medium size problems, and some computational results are described.
1.2K
References
A Rapidly Convergent Descent Method for Minimization
Roger Fletcher,M. J. D. Powell +1 more
TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
A Class of Methods for Solving Nonlinear Simultaneous Equations
TL;DR: In this article, the authors discuss certain modifications to Newton's method designed to reduce the number of function evaluations required during the iterative solution process of an iterative problem solving problem, such that the most efficient process will be that which requires the smallest number of functions evaluations.