No regularization backoff fo starting point

[atteson]

In trying to run my problem with Float32's (because I'm interesting in GPU execution), the regularization is failing in the computation of the starting point. Rather than backing off and increasing the regularization parameters, this just fails. In particular, it always chooses a fixed regD of 1e-6 which is small for Float32. My suggestion is that the starting point computation backoff and increase the regularization.

[mtanneau]

Thank you for using Tulip and for reporting this.
Would you be able to share a minimum working example please? I would expect the issue to occur on CPU as well.
I would need to be able to reproduce the error locally in order to understand the cause and issue a fix.

Small note: GPUs (at least the NIVIDA ones) should support Float64 execution.

[atteson]

Below is a minimum working example. I'm on Julia 1.10.5.

The GPU I'm working with is significantly slower on Float64 (perhaps an order of magnitude) than Float32.

using Tulip
using Random

Random.seed!(1)
nvar = 100
ncon = 1000
c = randn( Float32, nvar );
A = randn( Float32, ncon, nvar );
b = randn( Float32, ncon );

ipmdata = Tulip.IPMData( A, b, true, c, 0.0f0, zeros(Float32, length(c)), fill( Inf32, length(c) ) );
ipmoptions = Tulip.IPMOptions{Float32}()

kktoptions = Tulip.KKTOptions{Float32}(Tulip.KKT.TlpDense.Backend(), Tulip.KKT.K1())
mpc = Tulip.MPC( ipmdata, kktoptions );
@time Tulip.ipm_optimize!( mpc, ipmoptions )