Proximal Algorithms
Contents
11. Proximal Algorithms¶
11.1. Chapter Objectives¶
Proximal mappings
Existence and uniqueness of proximal mappings for proper, closed, convex functions
Proximal operators
11.2. Relevant results¶
We recall some results from previous chapters which will be helpful for the work in this chapter.
Sum of two closed functions is a closed function.
Some of a convex function with a strongly convex function is strongly convex.
A proper, closed and strongly convex function has a unique minimizer.
For some convex \(f: \RR \to \RERL\):
If \(f'(u) = 0\), then \(u\) must be one of its minimizers.
If the minimizer of \(f\) exists and is not attained at any point of differentiability, then it must be attained at a point of nondifferentiability.