quadform for positive semi-definite matrices

[JGSuw]

Hello Convex.jl community,

I am using Julia v1.4 and Convex v0.4.11 and apparently the function quadform currently does not support positive semi-definite nor negative semi-definite matrices. This is apparent from quadform.jl which uses the ispodef routine found in LinearAlgebra.jl to test for positive or negative definiteness.

Unfortunately this restriction is not reflected in the documentation for Convex.jl, which states that to use quadform "if x is not constant than P must be symmetric and positive semi-definite". Perhaps the documentation on supported operations was copy/pasted from another language where this functionality is present.

Regardless it is an unfortunate omission, since AFAIK that minimization QPs with positive semi-definite terms in the objective are still convex. Are they still not DCP?

Best,
Joseph Sullivan

[ericphanson]

Ah thanks for pointing this out. We actually just changed this code to use isposdef in #444 without realising the change in behaviour- that’s a bug which we should fix. So try Convex v0.14.10 for now (] add Convex@0.14.10). I’d be happy to take a PR to fix the bug, otherwise I can try to get to it in a bit.

[ericphanson]

As another workaround, you could also replace the matrix Q by Q + eps*I for small epsilon. I think that’s maybe how we should do the check anyway (ie check if Q + eps*I is positive definite).

[JGSuw]

Fantastic, thanks for the response. I will use an eps term to work around this, I'm glad that it will not actually cause any problems with the solvers.