JuMP: Hermitian matrix variable and complex numbers in model

ccoffrin · February 6, 2020, 12:24am

This is the place in PowerModels where the basic SDP relaxation constraint is added,

lanl-ansi/PowerModels.jl/blob/34fc00242deebf20c6f7eba45969f3a9d64f187a/src/form/wrm.jl#L25


      
              JuMP.@constraint(pm.model, [w_fr*c_rating_a^2+1, 2*p_fr, 2*q_fr, w_fr*c_rating_a^2-1] in JuMP.SecondOrderCone())
          
          
    p_to = var(pm, n, c, :p, t_idx)
              q_to = var(pm, n, c, :q, t_idx)
              JuMP.@constraint(pm.model, [w_to*c_rating_a^2+1, 2*p_to, 2*q_to, w_to*c_rating_a^2-1] in JuMP.SecondOrderCone())
          end
          
          

          

          
""
          function constraint_model_voltage(pm::AbstractWRMModel, n::Int, c::Int)
              _check_missing_keys(var(pm, n, c), [:WR,:WI], typeof(pm))
          
          
    WR = var(pm, n, c)[:WR]
              WI = var(pm, n, c)[:WI]
          
          
    JuMP.@constraint(pm.model, [WR WI; -WI WR] in JuMP.PSDCone())
          end
          
          

          
""

For a complex matrix W the encoding is, [\Re(W), \Im(W); -\Im(W), \Re(W)] \succeq 0. The Mosek manual is a fantastic refrence for SDP modeling tricks like this.