Submonotone mappings and the proximal point algorithm
Jonathan E. Spingarn · Numerical Functional Analysis and Optimization · 1982
The proximal point algorithm for solving 0 ε 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.