Michael J. D. Powell

Michael J. D. Powell's AcademicInfluence.com Rankings

Mathematics

#980

World Rank

#1695

Historical Rank

Measure Theory

#153

World Rank

#236

Historical Rank

mathematics Degrees

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Mathematics

Why Is Michael J. D. Powell Influential?

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According to Wikipedia, Michael James David Powell was a British mathematician, who worked in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. Education and early life Born in London, Powell was educated at Frensham Heights School and Eastbourne College. He earned his Bachelor of Arts degree followed by a Doctor of Science degree in 1979 at the University of Cambridge.

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Michael J. D. Powell's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A Rapidly Convergent Descent Method for Minimization (1963) (4309)
An efficient method for finding the minimum of a function of several variables without calculating derivatives (1964) (4103)
A fast algorithm for nonlinearly constrained optimization calculations (1978) (1764)
A method for nonlinear constraints in minimization problems (1969) (1597)
Radial basis functions for multivariable interpolation: a review (1987) (1439)
Restart procedures for the conjugate gradient method (1977) (1279)
The BOBYQA algorithm for bound constrained optimization without derivatives (2009) (1201)
A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation (1994) (1057)
Nonlinear Programming—Sequential Unconstrained Minimization Techniques (1969) (1026)
Approximation theory and methods (1984) (1013)
A Method for Minimizing a Sum of Squares of Non-Linear Functions Without Calculating Derivatives (1965) (673)
THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS (1978) (562)
Direct search algorithms for optimization calculations (1998) (528)
The NEWUOA software for unconstrained optimization without derivatives (2006) (502)
Algorithms for nonlinear constraints that use lagrangian functions (1978) (481)
Piecewise Quadratic Approximations on Triangles (1977) (457)
A New Algorithm for Unconstrained Optimization (1970) (434)
Variable Metric Methods for Constrained Optimization (1982) (433)
Nonconvex minimization calculations and the conjugate gradient method (1984) (403)
UOBYQA: unconstrained optimization by quadratic approximation (2002) (377)
CONVERGENCE PROPERTIES OF A CLASS OF MINIMIZATION ALGORITHMS (1975) (345)
The watchdog technique for forcing convergence in algorithms for constrained optimization (1982) (331)
On search directions for minimization algorithms (1973) (322)
On the Estimation of Sparse Jacobian Matrices (1974) (281)
A trust region algorithm for equality constrained optimization (1990) (244)
Convergence properties of algorithms for nonlinear optimization (1986) (198)
An Iterative Method for Finding Stationary Values of a Function of Several Variables (1962) (192)
On the global convergence of trust region algorithms for unconstrained minimization (1984) (191)
On the Convergence of the Variable Metric Algorithm (1971) (181)
On the quadratic programming algorithm of Goldfarb and Idnani (1985) (171)
A View of Algorithms for Optimization without Derivatives 1 (2007) (168)
Developments of NEWUOA for minimization without derivatives (2008) (148)
The uniform convergence of thin plate spline interpolation in two dimensions (1994) (137)
On the Estimation of Sparse Hessian Matrices (1979) (135)
Recent advances in unconstrained optimization (1971) (133)
A tolerant algorithm for linearly constrained optimization calculations (1989) (124)
Least Frobenius norm updating of quadratic models that satisfy interpolation conditions (2004) (124)
On trust region methods for unconstrained minimization without derivatives (2003) (121)
Univariate multiquadric approximation: Quasi-interpolation to scattered data (1992) (115)
A recursive quadratic programming algorithm that uses differentiable exact penalty functions (1986) (112)
Some convergence properties of the conjugate gradient method (1976) (106)
How bad are the BFGS and DFP methods when the objective function is quadratic? (1986) (99)
The Differential Correction Algorithm for Rational $\ell _\infty $-Approximation (1972) (97)
VMCWD: a Fortran subroutine for constrained optimization (1983) (95)
A Survey of Numerical Methods for Unconstrained Optimization (1970) (89)
Recent research at Cambridge on radial basis functions (1999) (83)
The differential correction algorithm for rational L∞ approximation (1971) (82)
On the Maximum Errors of Polynomial Approximations Defined by Interpolation and by Least Squares Criteria (1967) (81)
Radial basis function methods for interpolation to functions of many variables (2001) (74)
On applying Householder transformations to linear least squares problems (1968) (67)
Weighted Uniform Sampling — a Monte Carlo Technique for Reducing Variance (1966) (63)
Updating conjugate directions by the BFGS formula (1987) (59)
Nonlinear optimization, 1981 (1982) (59)
Optimization in action: 7th–9th January 1975. University of Bristol, UK. Organized by the Institute of Mathematics and its Applications, Essex, UK (1975) (58)
Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions (1999) (57)
Ground-State Splitting ford5S6Ions in a Cubic Field (1960) (57)
On fast trust region methods for quadratic models with linear constraints (2015) (51)
A calculation of the ground-state splitting for Mn2+ ions in a cubic field (1961) (51)
Least Squares Smoothing of Univariate Data to achieve Piecewise Monotonicity (1991) (50)
On the Modification of LDL T Factorizations (1974) (50)
Fast evaluation of polyharmonic splines in three dimensions (2006) (50)
A Krylov subspace algorithm for multiquadric interpolation in many dimensions (2005) (50)
On the convergence of trust region algorithms for unconstrained minimization without derivatives (2012) (45)
On the Lagrange functions of quadratic models that are defined by interpolation* (2001) (45)
On the modification of ^{} factorizations (1974) (41)
On the calculation of orthogonal vectors (1968) (41)
Tabulation of Thin Plate Splines on a Very Fine Two-Dimensional Grid (1992) (38)
On the use of quadratic models in unconstrained minimization without derivatives (2004) (37)
The convergence of variable metric matrices in unconstrained optimization (1983) (34)
Radial basis function interpolation on an infinite regular grid (1990) (31)
Developments of NEWUOA for unconstrained minimization without derivatives (2007) (31)
The Minimum Sum of Squares Change to Univariate Data that gives Convexity (1991) (30)
on The state of the art in numerical analysis (1987) (29)
Univariate Multiquadric Approximation: Reproduction of Linear Polynomials (1990) (27)
A View of Unconstrained Minimization Algorithms that Do Not Require Derivatives (1975) (24)
The State of the art in numerical analysis : proceedings of the Joint IMA/SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14-18 April 1986 (1988) (24)
On the number of iterations of Karmarkar's algorithm for linear programming (1993) (23)
Beyond symmetric Broyden for updating quadratic models in minimization without derivatives (2013) (22)
Univariate Multiquadric Interpolation: Some Recent Results (1991) (20)
The crystalline field parameters for dysprosium ethyl sulphate (1961) (19)
On the A-Acceptability of Rational Approximations that Interpolate the Exponential Function (1981) (19)
Karmarkar's algorithm : a view from nonlinear programming (1989) (18)
Some Convergence Properties of the Modified Log Barrier Method for Linear Programming (1995) (18)
Truncated Laurent expansions for the fast evaluation of thin plate splines (1993) (18)
On Best L 2 Spline Approximations (1968) (17)
On the convergence of the DFP algorithm for unconstrained optimization when there are only two variables (2000) (16)
A note on quasi-newton formulae for sparse second derivative matrices (1981) (15)
A Theorem on Rank One Modifications to a Matrix and Its Inverse (1969) (15)
The use of Band Matrices for Second Derivative Approximations in Trust Region Algorithms (1998) (14)
Perspectives on optimization : a collection of expository articles (1972) (14)
Extensions to subroutine VFO2AD (1982) (14)
An algorithm for maximizing entropy subject to simple bounds (1988) (14)
Quadratic Termination Properties of Minimization Algorithms I. Statement and Discussion of Results (1972) (13)
On updating the inverse of a KKT matrix 1 (2004) (13)
Necessary Conditions for a Minimax Approximation (1966) (12)
On error growth in the Bartels-Golub and Fletcher-Matthews algorithms for updating matrix factorizations (1987) (12)
A Technique that Gains Speed and Accuracy in the Minimax Solution of Overdetermined Linear Equations (1977) (11)
Log barrier methods for semi-infinite programming calculations (1993) (11)
An example of cycling in a feasible point algorithm (1981) (10)
System Modelling and Optimization (1999) (10)
The differential correction algorithm for generalized rational functions (1987) (10)
AN UPPER TRIANGULAR MATRIX METHOD FOR QUADRATIC PROGRAMMING (1981) (10)
On a decomposition of conditionally positive-semidefinite matrices☆ (1981) (9)
The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices (1981) (8)
System Modelling and Optimization: Methods, Theory and Applications, 19th IFIP TC7 Conference on System Modelling and Optimization, July 12-16, 1999, Cambridge, UK (2000) (8)
Conditions for Superlinear Convergence in l1 and l∞ Solutions of Overdetermined Non-linear Equations (1984) (8)
Quadratic termination properties of Davidon's new variable metric algorithm (1977) (7)
QR Factorization for Linear Least-Squares Problems on a Hypercube Multiprocessor (1988) (7)
On nonlinear optimization since 1959 (2009) (7)
Quadratic Termination Properties of Minimization Algorithms II. Proofs of Theorems (1972) (7)
A comparison of spline approximations with classical interpolation methods (1968) (6)
Five Lectures on Radial Basis Functions (2005) (6)
DAMTP 1999 / NA 11 Krylov subspace methods for radialbasis function interpolation 1 (5)
A 'taut string algorithm' for straightening a piecewise linear path in two dimensions (1998) (5)
On the Convergence of Cyclic Jacobi Methods (1975) (5)
On the convergence of a wide range of trust region methods for unconstrained optimization (2010) (5)
An Optimal Way of Moving a Sequence of Points onto a Curve in Two Dimensions (1999) (4)
Algorithms for Constrained and Unconstrained Optimization Calculations (1982) (4)
The Local Dependence of Least Squares Cubic Splines (2006) (3)
NA 05 Developments of NEWUOA for minimization without derivatives (2007) (3)
On the convergence of trust region algorithms for unconstrained minimization without derivatives (2012) (3)
Univariate Interpolation on a Regular Finite Grid by a Multiquadric Plus a Linear Polynomial (1992) (3)
Optimization algorithms in 1979 (1980) (3)
The Mathematical Programming Society (1977) (2)
THE EXCHANGE ALGORITHM FOR CALCULATING MINIMAX LINEAR APPROXIMATIONS OVER A DISCRETE POINT SET (1966) (2)
A discrete characterization theorem for the discrete L1 linear approximation problem (1980) (2)
On the Convergence of Exchange Algorithms for Calculating Minimax Approximations (1966) (2)
A TOLERANT ALGORITHM FOR LINEARLY CONSTRAINED (1989) (1)
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications (1999) (1)
On the Rate of Convergence of Variable Metric Algorithms for Unconstrained Optimization (2010) (1)
Derivate Free Optimization (2014) (1)
THE GENERAL THEORY OF LINEAR APPROXIMATION (1966) (1)
Trust Region Calculations Revisited 1 (1997) (0)
An application of gaussian elimination to interpolation by generalized rational functions (1984) (0)
A quadratic interpolation method for unconstrained minimization without derivatives (2000) (0)
Beyond symmetric Broyden for updating quadratic models in minimization without derivatives (2012) (0)
Erratum to: System Modelling and Optimization (1999) (0)
On fast trust region methods for quadratic models with linear constraints (2015) (0)
THEORY OF GENERAL NON-LINEAR MINIMAX APPROXIMATIONS (1966) (0)
On the Convergence of Multidirectional Search 23 (1991) (0)
Special Issue: The 3rd International Conference on Optimization Methods and Software (May 13-17, 2012, Chania, Greece) Foreword (2014) (0)
Book Review: Nonlinear Programming - Sequential Unconstrained Minimization Techniques, by A. V. Fiacco and G. P. McCormick, 1969; 210 pages (1969) (0)
DAMTP 1998 / NA 04 Direct search algorithms for optimizationcalculations (1998) (0)
On the Modification of LDII Factorizations (2010) (0)
Three lectures 1 on Derivative Free Optimization (2013) (0)
Panel discussion on multivariate problems (2005) (0)

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What Schools Are Affiliated With Michael J. D. Powell?

Michael J. D. Powell is affiliated with the following schools:

University of Cambridge