quadprog() is used for a very specific type of optimization problem and, therefore, can be optimized way more than fmincon(). However, note that there is no direct comparison since fmincon() can solve problems which quadprog() cannot. But for a similar problem, quadprog() will be faster. For example
H = [1 -1; -1 2];
f = [-2; -6];
A = [1 1; -1 2; 2 1];
b = [2; 2; 3];
opts1 = optimoptions('quadprog', 'Display', 'off');
opts2 = optimoptions('fmincon', 'Display', 'off');
t1 = timeit(@() quadprog(H, f, A, b, [], [], [], [], [], opts1))
t2 = timeit (@() fmincon(@(x) 1/2*x.'*H*x+f.'*x, rand(2,1), A, b, [], [], [], [], [], opts2))
Result
>> t1
t1 =
8.3352e-04
>> t2
t2 =
0.0081
>> t2/t1
ans =
9.6923
quadprog() is about 10 times faster. You can also check that both fmincon() and quadprog() give same solutions.
