Large-scale optimization

Test version of the LVMINI program

Efficient standard function minimization algorithms for optimization based on NEWTON steps require to calculate and store, among other arrays, the matrix of second derivatives with respect to the parameters, or the inverse matrix. For a large number n of parameters of the order of 100 000 this would require a very large memory space, larger than available on a standard PC. The gradient of the function (vector of first order derivatives) requires much less space. Simple steepest-descent minimization algorithms, requiring only the gradient, are usually rather slowly convergent or not converging at all. The L-BFGS (J. Nocedal) algorithm for large-scale minimization is a matrix-less quasi-NEWTON method. It allows to take advantage of the good convergence properties of the NEWTON methods without having to store the full matrix of second derivatives. It requires the calculation of the gradient and needs memory space for a small number of n-vectors.

LVMINI is a program package based on the L-BFGS algorithm. It requires a memory space for example of 52 Mbyte for 100 000 parameters. For a small number of parameters a calculation of parameter errors is included. It can be used for a small number of parameters down to 2 parameters, where it needs 34 double precision words (including the covariance matrix). Until now there is only a limited experience, and the program may fail for certain classes of problems

Program description

The software can be freely used for research and education. We expect that all publications describing work using this software quote at least one reference.

Disclaimer: This software is provided without any expressed or implied warranty. In particular there is no warranty of any kind concerning the fitness of this software for any particular purpose.

The LVMINI program package and a small test program, a makefile and the manual is in the file lvmini.tgz. Save the tgz file in a fresh subdirectory on your system. To install, first type

tar -xzf lvmini.tgz

make

./lvtest