Please follow this link to our website to review the limitation of QUADPROG:
The solution to indefinite or negative definite problems is often unbounded. In this case, "exitflag" is returned with a negative value to show a minimum was not found. Note that when a finite solution does exist, QUADPROG may only give local minima since the problem may still be nonconvex.
Try using the FMINCON function instead. Your objective function should be structured as:
myobjfun = @(x, H, c) (.5*x'*H*x + c'*x);
If you are using a version prior to MATLAB 7.0 (R14), you will need to create an inline function:
myobjfun = inline('(.5*x'*H*x + c'*x)', 'x', 'H', 'c');
The following function file computes the gradient of the quadratic and the first derivative matrix for the constraints, which in this case is just A':
function [g, gcon] = myg(x, H, c, A)
g = H*x + c;
gcon=A';
Then, FMINCON can be called using:
[x,optout] = fmincon(myobjfun, x0, A, b, [], [], lb, ub, @myg)
In general, QUADPROG should be preferred over FMINCON when possible, but for some particular problems, QUADPROG will not work.
