Chapter I A view of unconstrained optimization

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

[2]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

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

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

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

[6]  C. G. Broyden A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

[7]  John Grover Barnes,et al.  An Algorithm for Solving Non-Linear Equations Based on the Secant Method , 1965, Comput. J..

[8]  L. Armijo Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

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

[10]  C. Reinsch Smoothing by spline functions , 1967 .

[11]  Allen A. Goldstein,et al.  Constructive Real Analysis , 1967 .

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

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

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

[15]  A. V. Levy,et al.  Study on a supermemory gradient method for the minimization of functions , 1969 .

[16]  Lenhart K. Schubert Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian , 1970 .

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

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

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

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

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

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

[23]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[24]  P. Wolfe Convergence Conditions for Ascent Methods. II: Some Corrections , 1971 .

[25]  C. G. Broyden,et al.  The convergence of an algorithm for solving sparse nonlinear systems , 1971 .

[26]  W. E. Hart,et al.  Quasi-Newton Methods for Discretized Non-linear Boundary Problems , 1973 .

[27]  G. Stewart Introduction to matrix computations , 1973 .

[28]  John E. Dennis,et al.  On the Local and Superlinear Convergence of Quasi-Newton Methods , 1973 .

[29]  J. J. Moré,et al.  A Characterization of Superlinear Convergence and its Application to Quasi-Newton Methods , 1973 .

[30]  Philip E. Gill,et al.  Newton-type methods for unconstrained and linearly constrained optimization , 1974, Math. Program..

[31]  J. J. Moré,et al.  Quasi-Newton Methods, Motivation and Theory , 1974 .

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

[33]  S. W. Thomas Sequential estimation techniques for quasi-newton algorithms. , 1975 .

[34]  M. Powell CONVERGENCE PROPERTIES OF A CLASS OF MINIMIZATION ALGORITHMS , 1975 .

[35]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[36]  D. Goldfarb Factorized variable metric methods for unconstrained optimization , 1976 .

[37]  M. J. D. Powell,et al.  Restart procedures for the conjugate gradient method , 1977, Math. Program..

[38]  P. Toint On sparse and symmetric matrix updating subject to a linear equation , 1977 .

[39]  R. Schnabel,et al.  Solving Systems of Non-Linear Equations by Broyden&Apos;S Method with Projected Updates , 1977 .

[40]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[41]  Garth P. McCormick,et al.  A modification of Armijo's step-size rule for negative curvature , 1977, Math. Program..

[42]  P. Toint Some numerical results using a sparse matrix updating formula in unconstrained optimization , 1978 .

[43]  D. Heller A Survey of Parallel Algorithms in Numerical Linear Algebra. , 1978 .

[44]  R. Schnabel,et al.  Least Change Secant Updates for Quasi-Newton Methods , 1978 .

[45]  D. F. Shanno,et al.  Matrix conditioning and nonlinear optimization , 1978, Math. Program..

[46]  D. Shanno,et al.  Numerical comparison of several variable-metric algorithms , 1978 .

[47]  E. Marwil,et al.  Convergence Results for Schubert’s Method for Solving Sparse Nonlinear Equations , 1979 .

[48]  J. Dennis,et al.  Two new unconstrained optimization algorithms which use function and gradient values , 1979 .

[49]  Danny C. Sorensen,et al.  On the use of directions of negative curvature in a modified newton method , 1979, Math. Program..

[50]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

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

[52]  Jorge J. Moré,et al.  User Guide for Minpack-1 , 1980 .

[53]  A. Griewank Starlike domains of convergence for Newton's method at singularities , 1980 .

[54]  T. M. Williams,et al.  Practical Methods of Optimization. Vol. 1: Unconstrained Optimization , 1980 .

[55]  A. Griewank Analysis and modification of Newton's method at singularities , 1980 .

[56]  G. Moore,et al.  The Calculation of Turning Points of Nonlinear Equations , 1980 .

[57]  Kang C. Jea,et al.  Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods , 1980 .

[58]  D. G. Watts,et al.  Relative Curvature Measures of Nonlinearity , 1980 .

[59]  W. Murray,et al.  A Projected Lagrangian Algorithm for Nonlinear Minimax Optimization , 1980 .

[60]  R. Schnabel,et al.  A NEW DERIVATION OF SYMMETRIC POSITIVE DEFINITE SECANT UPDATES , 1980 .

[61]  C. Kelley,et al.  Newton’s Method at Singular Points. I , 1980 .

[62]  Jorge J. Moré,et al.  Algorithm 566: FORTRAN Subroutines for Testing Unconstrained Optimization Software [C5], [E4] , 1981, TOMS.

[63]  Andrzej STACHURSKI,et al.  Superlinear convergence of Broyden's boundedθ-class of methods , 1981, Math. Program..

[64]  Philippe L. Toint,et al.  Towards an efficient sparsity exploiting newton method for minimization , 1981 .

[65]  D. Sorensen An example concerning quasi-Newton estimation of a sparse hessian , 1981, SGNM.

[66]  David M. author-Gay Computing Optimal Locally Constrained Steps , 1981 .

[67]  W. Murray,et al.  A Projected Lagrangian Algorithm for Nonlinear $l_1 $ Optimization , 1981 .

[68]  W. Greub Linear Algebra , 1981 .

[69]  Philip E. Gill,et al.  Practical optimization , 1981 .

[70]  John E. Dennis,et al.  An Adaptive Nonlinear Least-Squares Algorithm , 1977, TOMS.

[71]  H. Walker,et al.  Convergence Theorems for Least-Change Secant Update Methods, , 1981 .

[72]  P. Toint,et al.  Local convergence analysis for partitioned quasi-Newton updates , 1982 .

[73]  Richard H. Byrd,et al.  A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties. , 1985 .

[74]  D. Sorensen Newton's method with a model trust region modification , 1982 .

[75]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[76]  P. Toint,et al.  Partitioned variable metric updates for large structured optimization problems , 1982 .

[77]  J. J. Moré,et al.  Newton's Method , 1982 .

[78]  A. Conn,et al.  An approach to nonlinear l1 data fitting , 1982 .

[79]  T. Steihaug The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[80]  Jorge J. Moré,et al.  Computing a Trust Region Step , 1983 .

[81]  J. J. Moré,et al.  Estimation of sparse jacobian matrices and graph coloring problems , 1983 .

[82]  M GayDavid,et al.  Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach , 1983 .

[83]  Albert G. Buckley,et al.  QN-like variable storage conjugate gradients , 1983, Math. Program..

[84]  Gene H. Golub,et al.  Matrix computations , 1983 .

[85]  R. Schnabel Quasi-Newton Methods Using Multiple Secant Equations. , 1983 .

[86]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

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

[88]  P. Toint,et al.  Optimal estimation of Jacobian and Hessian matrices that arise in finite difference calculations , 1984 .

[89]  Thomas F. Coleman,et al.  Software for estimating sparse Jacobian matrices , 1984, ACM Trans. Math. Softw..

[90]  R. Schnabel,et al.  Tensor Methods for Nonlinear Equations. , 1984 .

[91]  Thomas F. Coleman,et al.  Estimation of sparse hessian matrices and graph coloring problems , 1982, Math. Program..

[92]  S. Grzegórski Orthogonal Projections on Convex Sets for Newton-Like Methods , 1985 .

[93]  Robert B. Schnabel,et al.  Computational experience with confidence intervals for nonlinear least squares , 1986 .

[94]  Thomas F. Coleman,et al.  Software for estimating sparse Hessian matrices , 1985, TOMS.

[95]  A. Griewank On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions , 1985 .

[96]  Bobby Schnabel,et al.  A modular system of algorithms for unconstrained minimization , 1985, TOMS.

[97]  Daniel John Woods,et al.  An interactive approach for solving multi-objective optimization problems (interactive computer, nelder-mead simplex algorithm, graphics) , 1985 .

[98]  Homer F. Walker,et al.  Least-Change Sparse Secant Update Methods with Inaccurate Secant Conditions , 1985 .

[99]  H. Schwetlick,et al.  Numerical Methods for Estimating Parameters in Nonlinear Models With Errors in the Variables , 1985 .

[100]  J. Witmer,et al.  A Note on Parameter-Effects Curvature , 1985 .

[101]  Daniel J. Woods,et al.  Optimization on Microcomputers: The Nelder-Mead Simplex Algorithm , 1985 .

[102]  Carl Tim Kelley,et al.  Broyden’s Method for a Class of Problems Having Singular Jacobian at the Root , 1985 .

[103]  John L. Nazareth The method of successive affine reduction for nonlinear minimization , 1986, Math. Program..

[104]  R. Schnabel,et al.  Solving Systems of Nonlinear Equations by Tensor Methods. , 1986 .

[105]  Robert B. Schnabel,et al.  Concurrent Function Evaluations in Local and Global Optimization ; CU-CS-345-86 , 1987 .

[106]  Algorithms for Solving Sparse Nonlinear Systems of Equations , 1986 .

[107]  J. Flachs On the generation of updates for quasi-Newton methods , 1986 .

[108]  M. J. D. Powell,et al.  How bad are the BFGS and DFP methods when the objective function is quadratic? , 1986, Math. Program..

[109]  P. Toint,et al.  On Large Scale Nonlinear Least Squares Calculations , 1987 .

[110]  P. Boggs,et al.  A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression , 1987 .

[111]  J. Nocedal,et al.  Global Convergence of a Class of Quasi-newton Methods on Convex Problems, Siam Some Global Convergence Properties of a Variable Metric Algorithm for Minimization without Exact Line Searches, Nonlinear Programming, Edited , 1996 .

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

[113]  Douglas E. Salane A continuation approach for solving large-residual nonlinear least squares problems , 1987 .

[114]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[115]  Douglas M. Bates,et al.  A generalized Guass-Newton procedure for multi-response parameter estimation , 1987 .

[116]  J. Dennis,et al.  Generalized conjugate directions , 1987 .

[117]  David S. Bunch Maximum likelihood estimation of probabilistic choice methods , 1987 .

[118]  M. Lescrenier,et al.  Partially separable optimization and parallel computing , 1988 .

[119]  Richard H. Byrd,et al.  Approximate solution of the trust region problem by minimization over two-dimensional subspaces , 1988, Math. Program..

[120]  R. Tapia On secant updates for use in general constrained optimization , 1988 .

[121]  J. Dennis,et al.  A hybrid algorithm for solving sparse nonlinear systems of equations , 1988 .

[122]  Richard H. Byrd,et al.  Algorithm 676: ODRPACK: software for weighted orthogonal distance regression , 1989, TOMS.

[123]  J. Dennis,et al.  Convergence theory for the structured BFGS secant method with an application to nonlinear least squares , 1989 .