Incorrect solution of nonconvex QCP

Answered

Boshi Yang

July 25, 2023 16:19

• 
• 

We tried to solve a nonconvex quadratic program with quadratic constraints in the following form. 

min x'*Q*x + 2*q'*x
s.t. x'*x == 1, x'*B*x == 1

Gurobi provides an incorrect solution to the following data. 

Q =

    0.6504   -0.8572    0.5054   -0.6183
   -0.8572   -0.4829    0.2892    1.4221
    0.5054    0.2892   -0.3298   -0.2359
   -0.6183    1.4221   -0.2359    0.1547

B =

    2.0297    1.9554   -1.6496    2.6647
    1.9554    2.7037   -3.3201    1.7159
   -1.6496   -3.3201    5.1678   -1.0744
    2.6647    1.7159   -1.0744    7.5902

q =

    0.1626
    0.1190
    0.4984
    0.9597

The instance was run on a Macbook Pro. Gurobi 10.0.2 (Matlab 2022b) with default setting returns an optimal value of 0.2315, while the true optimal value is around -1.36. Has anyone observed similar issues? 

The Matlab code is posted below.

function result = TTRS_GRB(Q,q,B)
    
% Variable
n = length(q);
x = optimvar('x', n, 1);

% Objective
model.Q = sparse(Q);
model.obj = 2*q';
model.modelsense = 'min';

% Constraints
model.A = sparse(1,n);
model.b = 0;
model.quadcon(1).Qc = speye(n);
model.quadcon(1).q = sparse(n,1);
model.quadcon(1).rhs = 1;
model.quadcon(1).sense = '=';
model.quadcon(2).Qc = sparse(B);
model.quadcon(2).q = sparse(n,1);
model.quadcon(2).rhs = 1;
model.quadcon(2).sense = '=';

% Parameter
params.NonConvex = 2;
params.OutputFlag = 0;

% Solve
result = gurobi(model,params);

end

Related to

• Wrong Result

0

• 

  Marika Karbstein

  • Gurobi Staff

  July 26, 2023 06:30

  Please note that the default lower bound of the variables is 0. If you want to allow negative variable values, you need to set an appropriate lower bound.

  0

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