论文信息 - A Rapidly Convergent Descent Method for Minimization

A Rapidly Convergent Descent Method for Minimization

© The British Computer Society Issue Section: Articles Download all figures A powerful iterative descent method for finding a local minimum of a function of several variables is described. A number of theorems are proved to show that it always converges and that it converges rapidly. Numerical tests on a variety of functions confirm these theorems. The method has been used to solve a system of one hundred non-linear simultaneous equations. Related articles in Web of Science

Roger Fletcher | M. J. D. Powell | M. Powell | R. Fletcher

[1] R. Courant. Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[2] H. B. Curry. The method of steepest descent for non-linear minimization problems , 1944 .

[3] Kenneth Levenberg. A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[4] W. Heitler. The Principles of Quantum Mechanics , 1947, Nature.

[5] M. Hestenes,et al. Methods of conjugate gradients for solving linear systems , 1952 .

[6] A. Booth. Numerical Methods , 1957, Nature.

[7] George E. P. Box,et al. Evolutionary Operation: a Method for Increasing Industrial Productivity , 1957 .

[8] H. H. Rosenbrock,et al. An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[9] Garry J. Tee,et al. Iterative Methods for Linear Equations with Symmetric Positive Definite Matrix , 1961, Comput. J..

[10] Robert Hooke,et al. `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[11] M. J. D. Powell,et al. An Iterative Method for Finding Stationary Values of a Function of Several Variables , 1962, Comput. J..

[12] John A. Nelder,et al. A Simplex Method for Function Minimization , 1965, Comput. J..