Modelling of SOCP constraint and solving through CPLEX

Specific Domains Optimization (Mathematical)
,
1

Hello all, I am trying to implement and solve the following SOCP constraint through CPLEX solver

(cij)^2 + (sij)^2 <= cii*cjj

through Rotated Second Order cone as follows:

nSc = 10
nTP = 24
nBus = 34
nLines = 33
@variables(acopf,begin
        (c_ii[i=1:nSc, j=1:nTP,k=1:nBus])                                      
        (c_ij[i=1:nSc, j=1:nTP,k=1:nLines])                                   
        (s_ij[i=1:nSc, j=1:nTP,k=1:nLines])                                     
                 end

for s in 1:nSc 
     for t in 1:nTP 
          for i in 1:nLines
             aux_var = [sqrt(2)*cij[s,t,i],sqrt(2)*sij[s,t,i]]
             @constraint(acopf,[cii[s,t,i]; cii[s,t,i]; aux_var] in RotatedSecondOrderCone())
         end
     end
end

However, when I tried to solve it, I received the following error.

LoadError: Constraints of type MathOptInterface.VectorAffineFunction{Float64}-in-MathOptInterface.RotatedSecondOrderCone are not supported by the solver.

Definitely, there is something wrong in the implementation of the constraint. Can someone tell where is the mistake and how to implement this constraint?

2

How did you define acopf? Did you try adopt = Model(CPLEX.Optimizer)?

Otherwise, just write it as the quadratic form.

@constraint(acopf, 2 * cii[s,t,i] * cii[s,t,i] >= sum(x^2 for x in aux_var)