A bundle method using two polyhedral approximations of the epsilon-enlargement of a maximal monotone operator

Ludovic Nagesseur (1)

1 Mathématiques

In this work, we develop a variant of a bundle method in order to find a zero of a maximal monotone operator. This algorithm relies on two polyhedral approximations of the epsilon-enlargement of the considered operator, via a systematic use of the transportation formula. Moreover, the use of a double polyhedral approximation in our algorithm could inspire other bundle methods for the case where the given operator can be split as the sum of two other maximal monotone operators.

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Ludovic Nagesseur. A bundle method using two polyhedral approximations of the epsilon-enlargement of a maximal monotone operator. 2013. ⟨hal-00828930⟩