A Majorize-Minimize line search algorithm for barrier function

Emilie Chouzenoux (1) , Saïd Moussaoui (1) , J. Idier (1)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

Criteria containing a barrier function i.e., an unbounded function at the boundary of the feasible solution domain are frequently encountered in the optimization framework, in particular in interior point methods for constrained optimization. Barrier function has to be carefully handled in the optimization algorithm. When an iterative descent method is used for the minimization, a search along the line supported by the descent direction is usually performed at each iteration. However, standard line search strategies tend to be inefficient in this context. In this paper, we propose an original line search algorithm based on the majorize-minimize principle. A tangent majorant function is built to approximate a scalar criterion containing a barrier function. This leads to a simple line search ensuring the convergence of several classical descent optimization strategies. The practical efficiency of the proposal scheme is illustrated by means of an example of constrained quadratic programming.

Mots clés: optimisation; convergence; nonlinear conjugate gradient algorithm; interior point; linesearch; MM algorithm

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Emilie Chouzenoux, Saïd Moussaoui, J. Idier. A Majorize-Minimize line search algorithm for barrier function. 2009. ⟨hal-00362304v4⟩