Solving an SDP repeatedly where the matrix data changes in each repetition

Specific Domains Optimization (Mathematical)
6

I’d benchmark it first. You can also improve things by formulating the model close to the form that Mosek expects.

Use print_active_bridges(model) to see how we’re reformulating. Here’s a tutorial: Example: ellipsoid approximation · JuMP

You probably need something like this:

model = Model(Mosek.Optimizer)
@variable(model, X[1:m, 1:m], PSD)
@variable(model, y[1:n])
@variable(model, Z[1:m, 1:m], PSD)
@constraint(model, c_con, X + sum(y[i] * A[i] for i in 1:m) + B .== Z)

You could also benchmark doing something like:

for i in 1:m
    set_normalized_coefficient.(c_con, y[i], A_new[i])
end
set_normalized_rhs.(c_con, -B_new)

Note that you need -B because JuMP will move it to the right-hand side.

1 Like