Static optimization using fmincon and quadprog

Can anyone tell me which one os the optimization methods is faster between "fmincon" and "quadprog"? And why is it faster or slower?

Thanks in advance,

Raj Patel

Answer 1

[Ameer Hamza]

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.

[Raj Patel]

Thanks Ameer.

Raj Patel