The quadprog does not work as intended when the values in A matrix are very small. Is there any other method to deal with such problem?

Upon running the following code the quadprog gives the correct answer.

A = -1.0e-25*[0.1239,0.1302];
b = -349;
x = [0;0];

opts = optimoptions(@quadprog,'Display','off');

H = 2*eye(size(A,2));
f = zeros(size(A,2),1);

[vnew1, fval1] = quadprog(H, f, A, b, [],[], [], [] ,x,opts);

A*vnew1 <= 1.0*b        %for testing the output (logical 1 in this case)

However, when changing A matrix as follows, doesnot give right results:

A = -1.0e-50*[0.1239,0.1302];
b = -349;
x = [0;0];

opts = optimoptions(@quadprog,'Display','off');

H = 2*eye(size(A,2));
f = zeros(size(A,2),1);

[vnew1, fval1] = quadprog(H, f, A, b, [],[], [], [] ,x,opts);

A*vnew1 <= 1.0*b     % answer is logical 0 in this case.

Any suggestions to deal with such small values?

Answer 1

[Matt J]

I suggest you don't use such small values. Rewrite the problem so that your x(i) are measured in larger units, so that you will not need the factor of 1e-50.

The alternative is to adjust all of the optimoption tolerance parameters to be consistent with the unconventional scalings of your constraints and variables.

[John D'Errico]

Exactly. This is really just a problem of poor scaling. The solution? Avoid poor scaling, by scaling the variables and your problem so everything is a reasonable value. They invented picometers and light years for a good reason.