1. Partial inverse of a monotone operator
- Author
-
Jonathan E. Spingarn
- Subjects
Discrete mathematics ,Control and Optimization ,Applied Mathematics ,Hilbert space ,Monotonic function ,Strongly monotone ,Pseudo-monotone operator ,symbols.namesake ,Monotone polygon ,Multiplication operator ,symbols ,Unitary operator ,Subspace topology ,Mathematics - 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.
- Published
- 1983
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