| Article ID: | iaor20111392 |
| Volume: | 148 |
| Issue: | 1 |
| Start Page Number: | 107 |
| End Page Number: | 124 |
| Publication Date: | Jan 2011 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Johnstone A, Koch R, Lucet Yves |
We complete the study of the convexity of the proximal average by proving it is convex as a function of each of its parameters separately, but not jointly convex as a function of any two of its parameters. We present an interpolation‐based plotting algorithm that takes advantage of the partial convexity of the proximal average, and improves the plotting time by a factor of 100, while reducing picture sizes by a factor of 10.