Missing functions and calculus rules

[lostella]

This is a list of (some of the) currently missing functions and calculus rules for proximal mappings, with references. Please comment to add more to the list.

Functions

• [ ] Vapnik loss Bauschke and Combettes, 2nd ed, Example 24.29
• [x] Indicator of hyperslab, see Bauschke and Combettes, 2nd ed, Example 29.21
• [ ] Indicator of finite convex hull, see Bauschke and Combettes, 2nd ed, Example 29.26
• [x] Cubic Euclidean norm, see Beck, Example 6.20
• [ ] Negative Euclidean norm, see Beck, Example 6.21
• [ ] L1 norm over box, see Beck, Example 6.23
• [ ] Intersection of affine space and box Beck, Theorem 6.27
• [ ] Intersection of halfspace and box Beck, Example 6.32
• [ ] Intersection of L1 ball and box Beck, Example 6.34
• [ ] Sum of k largest values Beck, Example 6.50 <= THIS NEEDS FIXING, see sumLargest.jl
• [ ] Sum of k largest absolute values Beck, Example 6.51
• [ ] Phi and Bregman divergences, see here

Calculus rules

• [ ] Composition of even, smooth, convex function and distance from convex set, see Bauschke and Combettes, 2nd ed, Proposition 24.27
• [x] Prox of Moreau envelope, see Beck, Theorem 6.63
• [x] (#88) Epicomposition, see epicompose.jl
• [ ] Spectral functions, see Beck, Section 7
  • [ ] Schatten p-norms
  • [ ] Ky Fan k-norms

Notes

• Some rules require functions to be even, so adding an is_even property may be convenient.

[mkrishan]

EpiComposition: https://github.com/kul-forbes/ProximalOperators.jl/blob/master/src/calculus/epicompose.jl

I am not sure if we need phi and Bregman divergences as well.(https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8194899)

[lostella]

Well if they’re needed then they will be checked out sooner, otherwise they will stay longer on the list :-)

Added, thanks