Illustration of three piecewise convex functions.

Contexts in source publication

Context 1

... extension applies to the case when q = q m−1 is the left endpoint of Example 3.1 explains how to build surrogate functions for two popular piecewise convex functions in the optimization literature. It can be observed from the definition of surrogate functions and Figure 2 that surrogate functions always have a simpler geometric structure than the original f , so it is usually the case that proximal mapping associated with the surrogate functions have closedform expressions, given that proximal mapping associated with f has a closed-form solution. The proximal mappings associated with the surrogate functions are also given in Example 3.1. ...

Context 2

... extension applies to the case when q = q m−1 is the left endpoint of Example 3.1 explains how to build surrogate functions for two popular piecewise convex functions in the optimization literature. It can be observed from the definition of surrogate functions and Figure 2 that surrogate functions always have a simpler geometric structure than the original f , so it is usually the case that proximal mapping associated with the surrogate functions have closedform expressions, given that proximal mapping associated with f has a closed-form solution. The proximal mappings associated with the surrogate functions are also given in Example 3.1. ...