LSMMBarrier

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* author: Emilie Chouzenoux       		              *
* institution: LIGM -  Universite de Marne la Vallee  *
* date: Wednesday, March 04th 2013   	              *
* License CeCILL-B                                    *
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* RECOMMENDATIONS:                                  *
* This toolbox is designed to work with             *
* Matlab 7.0                                        *
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DESCRIPTION:
This toolbox allows to determine a suitable stepsize in iterative descent algorithms 
applied to the minimization of a criterion containing a logarithmic barrier function 
associated to linear constraints. A majorization-minimization (MM) scheme is adopted.
It is based on the derivation of a log-quadratic majorant function well suited to 
approximate the criterion containing barrier terms. The convergence of classical descent 
algorithms when this linesearch strategy is employed is ensured. 

A demo file illustrates the efficiency of the MM linesearch on the Newton minimization
of the barrier criterion associated to a random quadratic programming (QP) test problem.                     

This toolbox consists of 4 m-files:
1) MMBarrierLineSearch.m : performs the MM linesearch 
2) CoefMajorLog.m : derive the log-quadratic majorant parameters
3) demoQP.m : runs a quadratic programming example 
4) QuadPbMore.m : generates the QP problems 

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RELATED PUBLICATIONS:

# E. Chouzenoux, S. Moussaoui and J. Idier. "Majorize-Minimize Linesearch for Inversion 
Methods Involving Barrier Function Optimization." Inverse Problems, Vol. 28, No. 6, 2012.

# E. Chouzenoux, S. Moussaoui and J. Idier. "Efficiency of Line Search Strategies in Interior 
Point Methods for Linearly Constrained Optimization." In Proceedings of the IEEE Workshop on 
Statistical Signal Processing (SSP 2011), pages 101-104, Nice, France, 28-30 juin 2011.

# E. Chouzenoux, S. Moussaoui and J. Idier. "A Majorize-Minimize Line Search Algorithm 
for Barrier Function Optimization." In Proceedings of the 17th European Signal Processing 
Conference (EUSIPCO 2009), pages 1379-1383, Glasgow, UK, 24-28 aot 2009. EURASIP Press. 

QUADRATIC PROGRAMMING PROBLEMS GENERATION:

# Mor, J. J. et Toraldo, G. : "Algorithms for bound constrained quadratic programming problems."
Numerische Mathematik, 55:377400, 1989.

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