Also see DACE toolbox and Robust subroutines for non-linear optimization
August 2004: Some of the MATLAB functions have been collected (and updated) in the toolbox immoptibox
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Old function marquardt SMarquardt KMHybrid> SDogLeg> damp_newton linesearch ucminf splfit splval checkjacobi uctpget uctpval |
Toolbox function marquardt smarquardt nlshybrid nonlinsys dampnewton linesearch ucminf splinefit splineval checkgrad uctpget uctpval |
| A collection of MATLAB functions for solving
nonlinear
least squares problems. The methods are described in the lecture note Methods for Non-Linear Least Squares Problems For all the functions the introductory comment - as provided by help function should give sufficient information. For the sake of completeness a short user's guide is available Also see Auxiliary Programs |
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Marquardt's method
Available as marquardt.m
(for use when the Jacobian is available) and
SMarquardt.m
(the Jacobian is approximated).
Further documented in Damping
Parameter in Marquardt's Method, report IMM-REP-1999-05.
Hybrid method
Kaj Madsen's hybrid method
is available as KMHybrid.m
Further documented in K. Madsen (1988): A Combined Gauss-Newton
and Quasi-Newton Method for Non-Linear Least Squares. Institute for
Numerical Analysis (now part of IMM), DTU. Report NI-88-10.
Dog Leg Method
Powell's dog leg method for nonlinear systems of equations is available
as
DogLeg.m
(for use when the Jacobian is available) and
SDogLeg.m
(the Jacobian is approximated).
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| A collection of MATLAB functions
and Fortran subroutines
for finding an unconstrained minimizer of a general function, whose gradient
is available. The methods are described in the lecture note
Unconstrained Optimization For all the functions the introductory comment -as provided by help function should give sufficient information. For the sake of completeness a short user's guide is available. ucminf.m and ucminf.f are documented in UCMINF - an Algorithm for Unconstrained, Nonlinear Optimization Also see Auxiliary Programs |
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| conj_grad.m | Conjugate Gradient method. Choice between the Fletcher-Reeves and the
Polak-Ribiere version.
Needs linesearch . |
| damp_newton.m | Damped Newton method. The Hessian of the function must be provided. |
| quasi_newton.m | Quasi-Newton method. Choice between the DFP and the BFGS updating strategy.
Needs linesearch . |
| linesearch.m | Choice between exact and soft line search. |
| ucminf.m ucminf.f |
MATLAB and Fortran77 versions of the BFGS
method with soft line search and trust region type monitoring of
step length. The Fortran version needs minaux.f, see Auxiliary Programs |
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| Packages of programs in MATLAB and Fortran77
for interpolation and curve fitting with cubic splines.
For all functions the introductory comment should be a sufficient user's guide. |
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Fortran: The software consists of 4 files, and is available
as
fsplpak.tar.Z
Use the following Unix commands to install the software:
| uncompress fsplpak.tar.Z
tar -xvf fsplpak.tar rm fsplpak.tar |
The file TSPL.f contains a testing programme.
More information can be found in
H.B. Nielsen (1991): SPLPAK - Pascal and Fortran77 Subprograms
for Cubic Splines. Institute for Numerical Analysis (now part
of IMM), DTU. Report NI-91-06.
MATLAB : The software consists of 2 files,
| splfit.m | Fit (or interpolate) given data with a cubic spline, with or without end point constraints. | ||||||
| splval.m | For a given spline s this function can be used to evaluate
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| A MATLAB function for computing the parameters
of a model M(x,c,t) = c0 + c1 ex1 t + . . . cn exn t as a least squares fit to a set of data points. It is assumed that all the components are decaying, i.e. all xj are negative and that a starting guess on these exponents is available. The constant term c0 may be omitted. mexpfit.m The following auxiliary function is needed, qrfacsol.m The method is described in Separable NonLinear Least Squares, report IMM-REP-2000-01, and further documented in Multi-Exponential Fitting of Low-Field 1H NMR Data, report IMM-REP-2000-03. |
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| Program package in Fortran77 for computing the
l1-solution to
Ax "=" b .
The method is described in K. Madsen, H.B. Nielsen, A Finite Smoothing Algorithm for Linear l1 Estimation, SIAM J. on Optimization 3 (1993), 223-235. The software consists of 6 files. It is available as
The file readme.txt contains instructions.
More information can be found in
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Box Constrained Quadratic Programming
| Program package in Fortran77 for computing the minimizer
of q(y) = ½yTHy -
cTy
s.t. -e <= y <= e
The method is described in K. Madsen, H. B. Nielsen, M.C. Pinar,
Bound Constrained Quadratic Programming via Piecewise
Quadratic Functions, Mathematical Programming 85 (1) (1999).
Available as
Technical
Report The software consists of 5 files. It is available as
The file readme.txt contains instructions.
More information can be found in
H.B. Nielsen, QPBOX
USER'S GUIDE, A Fortran77 Package for Box Constrained Quadratic Programs,
Report IMM-REP-1997-04, Informatics and Mathematical Modelling, DTU. (1997),
14 pages.
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| checkjacobi.m
chkjac.f |
MATLAB function and Fortran77 subroutine
for checking the user's implementation
of the Jacobian (or gradient). More information can be found in Checking Gradients, available in pdf and ps format. 21.12.2000: New version of checkjacobi.m |
| qrfacsol.m | MATLAB function for computing and/or using a QR
factorization of a rectangular matrix . The tasks are Null space of A or AT Basic or minimum norm solution to A x "=" b Basic or minimum norm solution to ATx "=" b Basic or minimum norm solution to (ATA) x "=" b "=" means "approximately equal to" and the solution is found in the least squares sense. |
| uctpget.m uctpval.m uctp.f |
MATLAB functions and Fortran77 package for generating
test problems for unconstrained, nonlinear optimization. Information and User's guide can be found in UCTP - Test Problems for Unconstrained Optimization. Report IMM-REP-2000-17, Department of Mathematical Modelling, DTU. November 2000. |
| minaux.f | Fortran77 package with auxiliary subprograms, including a subset of the BLAS package. Is needed by the above ucminf.f and uctp.f. New version 21.12.2000. |
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