Warning: Solver not applicable (gurobi)

[碧尧邵]

I am solve a linear programming under a nonlinear constraints. I think the constraints are right and gurobi solver work for demo. However matlab post a error :Warning: Solver not applicable (gurobi). A part of my matlab code. 

Thanks in advance for anybody who can help me with this.

x = sdpvar(8,1);

lamda=sdpvar(size(line_1,1),2);

% K is a 3*3 matrix

K_1=inv(K);

F=[x(1)*x(5)+x(2)*x(6)+x(3)*x(7)==0 x(1)^2+x(2)^2+x(3)^2-1==0 x(5)^2+x(6)^2+x(7)^2-1==0];

f=0;

for i=1:size(line_1,1)

    % q is a 3*1 vector

    q=[line_1(i,:) 1]';

    % my objection is to min f

    f=f+abs(lamda(i,1)-lamda(i,2));

    % constraints

    F=[F [x(1) x(2) x(3)]*K_1*q*lamda(i,1)-x(4)==0 [x(5) x(6) x(7)]*K_1*q*lamda(i,2)-x(8)==0];

end

% optimize(F,f);

% ops = sdpsettings('solver', 'lpsolve', 'verbose', 2);

ops = sdpsettings('solver', 'gurobi');

result = solvesdp(F, f, ops);

double(x);

 

[Johan Löfberg]

Well, you already answered your self, the model is nonlinear. Gurobi is a linear solver

[碧尧邵]

Okay. Could you recommend some suitable solvers for this problem? Thank you so much!

[碧尧邵]

I choose fmincon function as solver because it is a nonlinear solver. Matlab post a problem:

Converged to an infeasible point.

fmincon stopped because the size of the current step is less than

the default value of the step size tolerance but constraints are not

satisfied to within the selected value of the constraint tolerance

here is the stopping criteria details:

Optimization stopped because the relative changes in all elements of x are

less than options.TolX = 1.000000e-10, but the relative maximum constraint

violation, 1.000000e+00, exceeds options.TolCon = 1.000000e-06.

[Johan Löfberg]

that's the problem with your model, it is nonconvex hence no guarantee that a local nonlinear solver will find any solution. try other local nonlnear solvers such as ipopt or knitro, or global nonlinear solvers such as bmibnb or baron

[Mark L. Stone]

Or try a non-default starting value, by using sdpsettings('usex0',1) and assign.

[碧尧邵]

I am confused about whether yalmip is suitable for building a nonlinear model with abs

[Johan Löfberg]

Sure, but with a caveat: If the abs operator i used in a non-convex fashion, YALMIP will derive a mixed-integer model of the absolute value.