Bounded Optimization by Quadratic Optimization

based on the C version by Éric Thiébaut, 2015-2017 https://github.com/emmt/Algorithms.git

based on the FORTRAN version by Mike Powell, 2009

This provides a C implementation of Mike Powell's BOBYQA algorithm for minimizing a function of many variables. The method is derivatives free (only the function values are needed) and accounts for bound constraints on the variables. The algorithm is described in:

M.J.D. Powell, "The BOBYQA Algorithm for Bound Constrained Optimization Without Derivatives." Technical report, Department of Applied Mathematics and Theoretical Physics, University of Cambridge (2009).

The present code is based on the original FORTRAN version written by Mike Powell who kindly provides his code on demand (at [email protected]) and has been converted to C by É. Thiébaut.

BOBYQA builds a quadratic model of the objective function from much less than (N+1)(N+2)/2 values of the function (with N the number of variables). The recommended number of points for building the quadratic model is 2*N+1. For smooth objective functions, BOBYQA is expected to be more efficient than COBYLA (which exploits a more simple linear model but implements arbitrary inequality constraints).

In addition to being usable from C code, this version of BOBYQA has a few improvements over the FORTRAN version:

• any objective function can be used (the function is an argument of the method) so different objective functions can co-exist in the same code (e.g. hierarchical optimization with BOBYQA is possible);

• a return code indicates the success of the method or the reason of the failure.

this version

by Daniel Pitzl, DESY, 2018

The simple Makefile uses the g++ compiler.
(no extern "C" {} in bobyqa.h)

make

The code consists in two files bobyqa.cc and bobyqa.h and is documented in the header bobyqa.h.

To build the library, edit the Makefile to suit your preferences and do:

make

A number of macros can defined for the compiler to adapt the type of variables used in the code (see bobyqa.h for details).

usage

include "bobyqa.h" in your project
add -L/your-path-to-bobyqa -lbobyqa to your Makefile
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/your-path-to-bobyqa

example

The test directory contains an example of least-squares fitting of a random-generated histogram to a Student's t distribution.

It uses ROOT from CERN for histogramming and visualization.

cd test
edit the Makefile: path to your ROOT installation
make
./student

initial:
fitted:

Hesse Eigenvalues  3.70176e+06  1.30337e+06  571758  441020  744.702
Hesse condition number  4970.8
Hesse Det  9.06005e+26

parameters: fitted values and uncertainties

par 0:  0.000619711 +- 0.00132251
par 1:  0.999723 +- 0.00159345
par 2:  3.03673 +- 0.0366171
par 3:  0.800951 +- 0.00132169
par 4:  0.202071 +- 0.00101357

parameter correlation matrix:

 0             1             2             3             4
 0    1    0.00346015    0.00287422     -0.001493    0.00159949
 1                  1       0.47594     -0.113242     0.0969192
 2                                1     -0.688977      0.766164
 3                                              1     -0.727242
 4                                                            1