Partial inverse of a monotone operator

Abstract

ForT a maximal monotone operator on a Hilbert spaceH andA a closed subspace ofH, the “partial inverse”T A ofT with respect toA is introduced.T A is maximal monotone. The proximal point algorithm, as it applies toT A , results in a simple procedure, the “method of partial inverses”, for solving problems in which the object is to findx ∈ A andy ∈ A ⊥ such thaty ∈ T(x). This method specializes to give new algorithms for solving numerous optimization and equilibrium problems.