Recent advances in unconstrained optimization

We survey the development of algorithms and theory for the unconstrained optimization problem during the years 1967–1970. Therefore (except for one remark) the material is taken from papers that have already been published. This exception is an explanation of some numerical difficulties that can occur when using Davidon's (1959) variable metric algorithm.

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

[2]  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..

[3]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[4]  J. M. Bennett.  Triangular factors of modified matrices , 1965 .

[5]  S. Goldfeld,et al.  Maximization by Quadratic Hill-Climbing , 1966 .

[6]  M. J. Box.  A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems , 1966, Comput. J..

[7]  J. F. Price,et al.  An effective algorithm for minimization , 1967 .

[8]  Willard I. Zangwill,et al.  Minimizing a function without calculating derivatives , 1967, Comput. J..

[9]  D. Winfield.  Function minimization without derivatives by a sequence of quadratic programming problems , 1967 .

[10]  G. W. Stewart,et al.  A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives , 1967, JACM.

[11]  C. G. Broyden.  Quasi-Newton methods and their application to function minimisation , 1967 .

[12]  Douglass J. Wilde,et al.  Foundations of Optimization. , 1967 .

[13]  J. Greenstadt.  On the relative efficiencies of gradient methods , 1967 .

[14]  Y. Bard.  On a numerical instability of Davidon-like methods , 1968 .

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

[16]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[17]  G. E. Myers.  Properties of the conjugate-gradient and Davidon methods , 1968 .

[18]  M. R. Osborne,et al.  Methods for unconstrained optimization problems , 1968 .

[19]  J. D. Pearson.  ON VARIABLE METRIC METHODS OF MINIMIZATION , 1968 .

[20]  J. W. Cantrell.  Relation between the memory gradient method and the Fletcher-Reeves method , 1969 .

[21]  P. Wolfe.  Convergence Conditions for Ascent Methods. II , 1969 .

[22]  J. D. Pearson.  Variable metric methods of minimisation , 1969, Comput. J..

[23]  Gerald Berman,et al.  Lattice Approximations to the Minima of Functions of Several Variables , 1969, JACM.

[24]  A. Miele,et al.  Study on a memory gradient method for the minimization of functions , 1969 .

[25]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[26]  G. McCormick.  THE RATE OF CONVERGENCE OF THE RESET DAVIDON VARIABLE METRIC METHOD , 1969 .

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

[28]  D. Shanno,et al.  Optimal conditioning of quasi-Newton methods , 1970 .

[29]  H. Y. Huang.  Unified approach to quadratically convergent algorithms for function minimization , 1970 .

[30]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[31]  M. Powell.  A Survey of Numerical Methods for Unconstrained Optimization , 1970 .

[32]  J. Greenstadt.  Variations on variable-metric methods. (With discussion) , 1970 .

[33]  Bruce A. Murtagh,et al.  Computational Experience with Quadratically Convergent Minimisation Methods , 1970, Comput. J..

[34]  A. Miele,et al.  Memory gradient method for the minimization of functions , 1970 .

[35]  Yonathan Bard,et al.  Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation Problems , 1970 .

[36]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[37]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm , 1970 .

[38]  D. Shanno.  Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[39]  J. Greenstadt.  Variations on Variable-Metric Methods , 1970 .

[40]  D. Goldfarb.  A family of variable-metric methods derived by variational means , 1970 .

[41]  M. Powell.  On the Convergence of the Variable Metric Algorithm , 1971 .