Convex conjugacy gives a one to one correspondence between proper, lower semicontinuous, convex functions and their (proper, lower semicontinuous, convex) conjugates. The operations of adding two functions and of multiplying a function by a constant are reflected, through convex conjugacy, in operations involving epigraphs: epi-addition (also called inf-convolution) and epi-multiplication.
The talk will present how the operations mentioned above can be combined to:
In particular, a self-dual approximation technique and a self-dual "proximal average" will be described. Self-duality here means that the conjugate of the approximate is the approximate of the conjugate, and that the conjugate of the proximal average is the proximal average of conjugates.