Replace exponential cone projection?

[tjdiamandis]

There's a new, robust implementation of the projection onto the exponential cone detailed in this paper by Henrik Friberg.

This is implemented in MathOptSetDistances.jl. Happy to port over.
https://github.com/matbesancon/MathOptSetDistances.jl/blob/1f3e578398ba91fbbcaf805aaf55f9105d858a40/src/projections.jl#L170

Relevant section of code:

ProximalOperators.jl/src/functions/indExp.jl

Line 79 in 7889da3

function prox!(y::AbstractVector{R}, f::IndExpPrimal, x::AbstractVector{R}, gamma::R=R(1)) where R <: Real

[lostella]

Very interesting! I think it would be nice to replace the current implementation. For reference, some test cases on this projection can be found here:

ProximalOperators.jl/test/test_results.jl

Line 196 in 7889da3

Dict( "f" => IndExpPrimal(),

[lostella]

This could be the occasion to first add benchmarks for the projection on the exponential cone, so to “touch with hand” the performance improvement https://github.com/JuliaFirstOrder/ProximalOperators.jl/blob/master/benchmark/benchmarks.jl

[lostella]

Benchmarks being added in #126