Proximal Algorithm Meets a Conjugate descent

Matthieu Kowalski (1)

1 L2S - Laboratoire des signaux et systèmes

This paper proposes an enhancement of the non linear conjugate gradient algorithm for some non-smooth problems. We first extend some results of descent algorithms in the smooth case for convex non-smooth functions. We then construct a conjugate descent algorithm based on the proximity operator to obtain a descent direction. We finally provide a convergence analysis of this algorithm, even when the proximity operator must be computed by an iterative process.

Mots clés: non smooth optimization; conjugate descent algorithm; proximal algorithm

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

Matthieu Kowalski. Proximal Algorithm Meets a Conjugate descent. 2010. ⟨hal-00505733v2⟩