Michael J. D. Powell. 29 July 1936—19 April 2015

Michael James David Powell was a British numerical analyst who was among the pioneers of computational mathematics. During a long and distinguished career, first at the Atomic Energy Research Establishment (AERE) Harwell and subsequently as the John Humphrey Plummer Professor of Applied Numerical Analysis in Cambridge, he contributed decisively towards establishing optimization theory as an effective tool of scientific enquiry, replete with highly effective methods and mathematical sophistication. He also made crucial contributions to approximation theory, in particular to the theory of spline functions and of radial basis functions. In a subject that roughly divides into practical designers of algorithms and theoreticians who seek to underpin algorithms with solid mathematical foundations, Mike Powell refused to follow this dichotomy. His achievements span the entire range from difficult and intricate convergence proofs to the design of algorithms and production of software. He was among the leaders of a subject area that is at the nexus of mathematical enquiry and applications throughout science and engineering.

[1]  M. J. D. Powell,et al.  UOBYQA: unconstrained optimization by quadratic approximation , 2002, Math. Program..

[2]  M. J. D. Powell.  Univariate Multiquadric Approximation: Reproduction of Linear Polynomials , 1990 .

[3]  Alexander H. G. Rinnooy Kan,et al.  Preface : Current developments in the interface economics, econometrics, mathematics , 1982 .

[4]  M. Powell.  A New Algorithm for Unconstrained Optimization , 1970 .

[5]  M. J. D. Powell,et al.  Beyond symmetric Broyden for updating quadratic models in minimization without derivatives , 2013, Math. Program..

[6]  M. J. D. Powell,et al.  VMCWD: a Fortran subroutine for constrained optimization , 1983, SMAP.

[7]  M. J. D. Powell,et al.  On the convergence of the DFP algorithm for unconstrained optimization when there are only two variables , 2000, Math. Program..

[8]  M. J. D. Powell.  Univariate Multiquadric Interpolation: Some Recent Results , 1991, Curves and Surfaces.

[9]  M. J. D. Powell,et al.  Algorithms for nonlinear constraints that use lagrangian functions , 1978, Math. Program..

[10]  Ya-Xiang Yuan,et al.  A recursive quadratic programming algorithm that uses differentiable exact penalty functions , 1986, Math. Program..

[11]  M. J. D. Powell,et al.  An Optimal Way of Moving a Sequence of Points onto a Curve in Two Dimensions , 1999, Comput. Optim. Appl..

[12]  Larry L. Schumaker,et al.  Numerical Methods in Approximation Theory, Vol. 9 , 1992 .

[13]  M. J. D. Powell,et al.  A comparison of spline approximations with classical interpolation methods , 1968, IFIP Congress.

[14]  M. J. D. Powell,et al.  On the number of iterations of Karmarkar's algorithm for linear programming , 1993, Math. Program..

[15]  William C. Davidon,et al.  Variance Algorithm for Minimization , 1968, Comput. J..

[16]  M. J. D. Powell,et al.  A Method for Minimizing a Sum of Squares of Non-Linear Functions Without Calculating Derivatives , 1965, Comput. J..

[17]  M. Powell.  A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 1994 .

[18]  Malcolm A. Sabin,et al.  Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[19]  M. Powell.  The uniform convergence of thin plate spline interpolation in two dimensions , 1994 .

[20]  M. Powell,et al.  Tabulation of Thin Plate Splines on a Very Fine Two-Dimensional Grid , 1992 .

[21]  David A. H. Jacobs,et al.  The State of the Art in Numerical Analysis. , 1978 .

[22]  M. Powell,et al.  Conditions for Superlinear Convergence in l1 and l∞ Solutions of Overdetermined Non-linear Equations , 1984 .

[23]  M. Powell,et al.  Approximation theory and methods , 1984 .

[24]  M. Powell,et al.  On the Estimation of Sparse Jacobian Matrices , 1974 .

[25]  M. J. D. Powell,et al.  On the global convergence of trust region algorithms for unconstrained minimization , 1984, Math. Program..

[26]  M. Powell,et al.  Radial basis function interpolation on an infinite regular grid , 1990 .

[27]  M. J. D. Powell.  The Local Dependence of Least Squares Cubic Splines , 2006 .

[28]  M. J. D. Powell,et al.  The Minimum Sum of Squares Change to Univariate Data that gives Convexity , 1991 .

[29]  M. J. D. Powell,et al.  On the Convergence of Cyclic Jacobi Methods , 1975 .

[30]  R. Beatson,et al.  Fast evaluation of polyharmonic splines in three dimensions , 2006 .

[31]  M. J. D. Powell,et al.  Least Frobenius norm updating of quadratic models that satisfy interpolation conditions , 2004, Math. Program..

[32]  M. J. D. Powell,et al.  A note on quasi-newton formulae for sparse second derivative matrices , 1981, Math. Program..

[33]  M. J. D. Powell.  On the convergence of a wide range of trust region methods for unconstrained optimization , 2010 .

[34]  M. J. D. Powell,et al.  Least Squares Smoothing of Univariate Data to achieve Piecewise Monotonicity , 1991 .

[35]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[36]  M. Powell,et al.  The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices , 1981 .

[37]  M. J. D. Powell,et al.  Direct search algorithms for optimization calculations , 1998, Acta Numerica.

[38]  M. J. D. Powell,et al.  On fast trust region methods for quadratic models with linear constraints , 2015, Math. Program. Comput..

[39]  Ya-Xiang Yuan,et al.  A trust region algorithm for equality constrained optimization , 1990, Math. Program..

[40]  Martin Grötschel,et al.  Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 , 1983, ISMP.

[41]  M. J. D. Powell,et al.  On the use of quadratic models in unconstrained minimization without derivatives , 2004, Optim. Methods Softw..

[42]  M. J. D. Powell,et al.  Updating conjugate directions by the BFGS formula , 1987, Math. Program..

[43]  M. J. D. Powell.  Truncated Laurent expansions for the fast evaluation of thin plate splines , 2005, Numerical Algorithms.

[44]  J. Herskovits.  A View on Nonlinear Optimization , 1995 .

[45]  M. J. D. Powell,et al.  Some Convergence Properties of the Modified Log Barrier Method for Linear Programming , 1995, SIAM J. Optim..

[46]  M. J. D. Powell,et al.  On the convergence of trust region algorithms for unconstrained minimization without derivatives , 2012, Comput. Optim. Appl..

[47]  M. Powell.  Log barrier methods for semi-infinite programming calculations , 1993 .

[48]  M. Powell,et al.  On the A-Acceptability of Rational Approximations that Interpolate the Exponential Function , 1981 .

[49]  M. J. Powell,et al.  The volume internal to three intersecting hard spheres , 1964 .

[50]  M. Powell.  Karmarkar's algorithm : a view from nonlinear programming , 1989 .

[51]  M. Powell,et al.  On the Estimation of Sparse Hessian Matrices , 1979 .

[52]  M. J. D. Powell,et al.  An example of cycling in a feasible point algorithm , 1981, Math. Program..

[53]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[54]  M. Powell.  A View of Algorithms for Optimization without Derivatives 1 , 2007 .

[55]  M. J. D. Powell,et al.  On search directions for minimization algorithms , 1973, Math. Program..

[56]  M. J. D. Powell,et al.  On trust region methods for unconstrained minimization without derivatives , 2003, Math. Program..