A Primal-Dual Method of Partial Inverses for Composite Inclusions

Maryam A. Alghamdi (1) , Abdullah Alotaibi (1) , Patrick Louis Combettes (2) , Naseer Shahzad (1)

1 Department of Mathematics [Jeddah]
2 LJLL - Laboratoire Jacques-Louis Lions

Spingarn’s method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the partial inverse formalism. The versatility of the resulting primal-dual splitting algorithm is illustrated through applications to structured monotone inclusions and optimization.

Mots clés: convex optimization; duality; method of partial inverses; monotone operator; splitting algorithm

Domaines: Analyse numérique [cs.NA]

Maryam A. Alghamdi, Abdullah Alotaibi, Patrick Louis Combettes, Naseer Shahzad. A Primal-Dual Method of Partial Inverses for Composite Inclusions. Optimization Letters, 2015, Optimization Letters, 8 (8), pp.2271-2284. ⟨hal-01158985⟩