Adding lazy cuts to an LP using JuMP.@build_constraint

Specific Domains Optimization (Mathematical)
3

You omitted my innermost break? Don’t quite understand.
I take your point on not using @build_constraint.
It is a folklore that Dict can be slow (here), therefore I thought use Array could be faster. (#undef will not occupy my memory?)
And I use the name exists_violation because I may execute many blocks of this lazy-cut (thus it is not necessarily feasible after only one batch).
Finally, I suspect that findall might be a bit lengthy

Therefore I think it might be better to loop directly.
In a 2-dimensional case, the revised code might look like this

is_cd_idle, cd_ref = trues(M, N), Matrix{JuMP.ConstraintRef}(undef, M, N)
while true
    exists_violation = false
    for i in 1:is_cd_idle.dims[1], j in 1:is_cd_idle.dims[2]
        is_cd_idle[i, j] || continue
        R_x[i, j] + DI[i] - DJ[j] < -COT || continue
        exists_violation = true
        is_cd_idle[i, j], cd_ref[i, j] = false, JuMP.@constraint(lpr, R_x[i, j] + lpr_DI[i] - lpr_DJ[j] >= 0)
        solve_to_normality(lpr)
        DI, DJ = JuMP.value.(lpr_DI), JuMP.value.(lpr_DJ)
        break
    end
    exists_violation || break # add how many cuts = sum(.!(is_cd_idle))
end
@info "after adding $(count((.!is_cd_idle))) cuts, there is no more violation"