No feasible solution found when using quadprog

Hello,

I am dealing with a large-scale convex quadratic programming with onlu inequality constraint.

In particular, H is a 1516-square matrix and A has dimension of 3038x1516.

I have used the code:

options = optimoptions('quadprog','interior-point-convex');
[x,fval,exitflag,output,lambda] = quadprog(H,f,A,b,[],[],[],[],[],options);

but the output is:

No feasible solution found.

quadprog stopped because it was unable to find a point that satisfies
the constraints within the default value of the constraint tolerance.

I have tried to normalize the matrix A and the vector b (as suggested in a old thread) but I got the same output. Then, using the suggestions of Converged to an Infeasible Point at https://it.mathworks.com/help/optim/ug/when-the-solver-fails.html#br44i73, I have tried to let Matlab find a feasible solution using LinProg and settingthe objective function to zero. Even in this way the solver cannot find a fesible solution. But, the vector of all zeros and of all ones are two fesible points.

Any suggestions?

Thank you a lot-

[Bruno Luong]

"But, the vector of all zeros and of all ones are two fesible points. "

What is you provide those vectors as x0?

[Elisabetta Biondi]

Do you mean to use not the interior point? I have tried with 'Active-set' and 'x0' equal to zeros. But it gives me:

Exiting: the constraints are overly stringent;
 no feasible starting point found. 

Actually, I have checked that the ones is not fesible (I was wrong).

[Bruno Luong]

If you said "all zeros and of all ones are two fesible points" then if you provide them as starting point, quadprog should never "stopped because it was unable to find a point that satisfies the constraints", but of course you have to use whatever algorithm that accepts starting point.

Unless if you make a mistake in setting up your problem. It's just a way to make sure there is no problem of your input arguments passing to quadprog.

[Matt J]

I suggest attaching a.mat file containing b and c=sum(A,2).

[Matt J]

I have used the code:

I doubt it. The first line generates an error.

options = optimoptions('quadprog','interior-point-convex');

Error using optimoptions (line 121)
Option 'interior-point-convex' does not have a value.

[Elisabetta Biondi]

Sorry, I have discovered that was an error in the matrix, and finally the output is:

Minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the default value of the optimality tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.

However, if I compute sum(A*x-b<=0), it turns out that the point is not fesible.

In the following a provide a .mat file with b and c=sum(A,2).

[Bruno Luong]

Your b contain -1, so zeros is NOT feasible point either. (since A*0 is 0 vector and it is NOT <= -1)

You seem to have bug in b, or do your formulation incorrectky.

[Elisabetta Biondi]

I upload again the mat file, because actually my b has 0 as minimum