1. Submonotone mappings and the proximal point algorithm
- Author
-
Jonathan E. Spingarn
- Subjects
Discrete mathematics ,Class (set theory) ,Control and Optimization ,Property (philosophy) ,Mathematics::Optimization and Control ,Computer Science Applications ,Proximal point ,Monotone polygon ,Signal Processing ,Minification ,Convex function ,Algorithm ,Analysis ,Mathematics - Abstract
The proximal point algorithm for solving 0 e T(x) with T maximal monotone is extended to mappings T satisfying the weaker property of maximal strict hypomonotonicity. The algorithm is applied to the minimization of a certain class of nondifferentiable nonconvex functions, the lower-C2 functions., whose subdifferentials are maximal strictly hypomonotone. For functions in this class, each step of the algorithm consists in minimizing a convex function.
- Published
- 1982
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