Unbounded objective function

[Redkaido]

I run the code, it shows that YALMIP problem 2 'Unbounded objective function (GUROBI)'
Meanwhile, I have constrained the lb and ub of parameters, but I check lb and ub of model are inf.
Please help me to solve the problems. Thank you.

The matlab code is as follows.

  base=4;
  use=3;
  SNR0 = 100;
  B=499.2e6;
  c = physconst('LightSpeed'); 
  %parameter
  baseloc=intvar(base, 3, 'full');
  useloc=intvar(use, 3, 'full');
  %intermedia
  H=sdpvar(use*base,7, 'full');
  C=sdpvar(7,7);

 cons=[0<=baseloc(1,1)<=500];
 cons=[cons 0<=baseloc(1,2)<=300];
 cons=[cons 0<=baseloc(1,3)<=1500];
 cons=[cons 0<=baseloc(2,1)<=500];
 cons=[cons 0<=baseloc(2,2)<=300];
 cons=[cons 0<=baseloc(2,3)<=1500];
 cons=[cons 0<=baseloc(3,1)<=500];
 cons=[cons 0<=baseloc(3,2)<=300];
 cons=[cons 0<=baseloc(3,3)<=1500];
 cons=[cons 0<=baseloc(4,1)<=500];
 cons=[cons 0<=baseloc(4,2)<=300];
 cons=[cons 0<=baseloc(4,3)<=1500];

 cons=[cons 0<=useloc(1,1)<=4600];
 cons=[cons 400<=useloc(1,2)<=520];
 cons=[cons 200<=useloc(1,3)<=1600];
 cons=[cons 0<=useloc(2,1)<=4600];
 cons=[cons 400<=useloc(2,2)<=520];
 cons=[cons 200<=useloc(2,3)<=1600];
 cons=[cons 0<=useloc(3,1)<=4600];
 cons=[cons 400<=useloc(3,2)<=520];
 cons=[cons 200<=useloc(3,3)<=1600];

  for i=1:base
      for j=i+1:base
          cons=[cons sum((baseloc(i,:)-baseloc(j,:)).^2)>=1];
      end
  end
  for i=1:use
      for j=i+1:use
          cons=[cons sum((useloc(i,:)-useloc(j,:)).^2)>=1];
      end
  end
  
  for i=1:3
      cons=[cons sum((baseloc(2:end,i)-kron(ones(base-1,1),baseloc(1,i))).^2)>=1];
      cons=[cons sum((useloc(2:end,i)-kron(ones(use-1,1),useloc(1,i))).^2)>=1];
  end
  centerLoc0=[2300,1300,800];

q=[0,0,0,1];
qin1 = [2 * q(1) 2 * q(2) 2 * q(3);
        2 * q(2) -2 * q(1) -2 * q(4);
        2 * q(3) 2 * q(4) -2 * q(1)];
qin2 = [-2 * q(2) 2 * q(1) 2 * q(4);
        2 * q(1) 2 * q(2) 2 * q(3);
        -2 * q(4) 2 * q(3) -2 * q(2)];
qin3 = [-2 * q(3) -2 * q(4) 2 * q(1);
        2 * q(4) -2 * q(3) 2 * q(2);
        2 * q(1) 2 * q(2) 2 * q(3)];
qinw = [2 * q(4) -2 * q(3) 2 * q(2);
        2 * q(3) 2 * q(4) -2 * q(1);
        -2 * q(2) 2 * q(1) 2 * q(4)];
for idx=1:use
    for jdx=1:base
     %H
cons=[cons,H(base*idx+jdx-base,:)==[(15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,:) - baseloc(jdx,:)) * (qin1 * (useloc(idx,:)-centerLoc0)'/1000) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000),...
    (15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,:) - baseloc(jdx,:)) * (qin2 * (useloc(idx,:)-centerLoc0)'/1000) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000),...
    (15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,:) - baseloc(jdx,:)) * (qin3 * (useloc(idx,:)-centerLoc0)'/1000) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000),...
    (15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,:) - baseloc(jdx,:)) * (qinw * (useloc(idx,:)-centerLoc0)'/1000) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000),...
    (15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,1) - baseloc(jdx,1)) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000),...
    (15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,2) - baseloc(jdx,2)) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000),...
    (15.55 -20*log10(sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2)/1000/1000)) *(useloc(idx,3) - baseloc(jdx,3)) / ((sum((baseloc(jdx,:) - useloc(idx,:)).^2, 2))^(0.5)/1000)]];    
    end
end
cons=[cons, C*(H'*H)==eye(7)];
Obj=trace(C); %trace((H'H)^-1)

ops = sdpsettings('solver','gurobi+','verbose',2,'gurobi.NonConvex',2,'gurobi.ResultFile','MyFile.lp','debug',1);
ops.gurobi.TuneTimeLimit = 0;
result = optimize(cons, Obj, ops);
if result.problem==0
      value(x)
      value(Obj)
else
     [model,recoverymodel] = export(cons, Obj, ops);
end

[johanlofberg]

This problem cannot be solved using gurobi. You are forcing yalmip to send the model to gurobi, despite gurobi having no clue what do with it (by using 'gurobi+')

[johanlofberg]

In YALMIP none, needs better formulation

[Redkaido]

Dear prof. Johan,

Excuse me.
If I changed the OBJ=norm(H). Can I use YALMIP to get the optimum?

Thank you.
Jun,
NTU

[johanlofberg]

Depends on what context you are talking about. With gurobi, norm(H) is reasonable as it is directly socp representable. For a nonlinear solver, it is a bad model, since nonlinear solvers don't like socp models, and should thus simply use the quadratic objective H'*H

[Redkaido]

Thank you very much.
The objective has better directly socp. The Obj=det(H'*H) is also unavailable?

[johanlofberg]

there is no way to get that into a nice form https://yalmip.github.io/tutorial/maxdetprogramming/