Log determinant objective

#1

Any recommendations on how to formulate a log determinant objective in JuMP? Thanks.

#2

The current recommendation is to use the log-det cone:
http://www.juliaopt.org/MathOptInterface.jl/stable/apireference/#MathOptInterface.LogDetConeTriangle
It is automatically reformulated into exponential cone and PSD constraints with
http://www.juliaopt.org/MathOptInterface.jl/stable/apireference/#MathOptInterface.Bridges.LogDetBridge
To maximize the volume of an ellipsoid with rotated second-order cone (RSOC) instead of exponential cone, there is also
http://www.juliaopt.org/MathOptInterface.jl/stable/apireference/#MathOptInterface.RootDetConeTriangle
which is automatically reformulated into RSOC and PSD constraints with
http://www.juliaopt.org/MathOptInterface.jl/stable/apireference/#MathOptInterface.Bridges.RootDetBridge
Some solvers such as https://github.com/blegat/SDPT3.jl supports having log-det in the objective directly but this package is not finished yet.

I have created a package to make it easy write optimization problems with ellipsoids: https://github.com/blegat/SetProg.jl
See https://www.youtube.com/watch?v=hV3G-eNLNjk

3 Likes
#3

Thanks! I will look into it.