Setting up the problem

In MATLAB we define the problem as

% Define the problem
H = eye(2);
f = [1;1]; 
A = [1 2; 1 -1];
bupper = [1; 2; 3; 4];
blower = [-1; -2; -3; -4];
sense = zeros(4,1,'int32');

sense determines the type of the constraints (more details are given here).

Note: When \(b_u\) and \(b_l\) have more elements than the number of rows in \(A\), the first elements in \(b_u\) and \(b_l\) are interpreted as simple bounds.

Calling DAQP

There are two ways of calling DAQP in MATLAB. The first way is through a quadprog call:

[x,fval,exitflag,info] = daqp.quadprog(H,f,A,bupper,blower,sense);

This will solve the problem with default settings. A more flexible interface is also offered, where we first setup the problem and then solve it:

d = daqp();
d.setup(H,f,A,bupper,blower,sense);
[x,fval,exitflag,info] = d.solve();

This allows us to reuse internal matrix factorization if we want to solve a perturbed problem.

Changing settings

If we, for example, want to change the maximum number of iterations to 2000 we can do so by

d.settings('iter_limit',2000)

A full list of available settings is provided here.

Using DAQP in YALMIP

DAQP can also be interfaced to YALMIP. The following code sets up and solves the problem considered above

% Setup problem
x = sdpvar(2,1);
cons = [-1 <= x(1) <=1,...
        -2 <= x(2) <=2,...
        -3 <= x(1)+2*x(2) <= 3,...
        -4 <= x(1)-x(2) <= 4];
obj = 0.5*x'*x+x(1)+x(2);
options = sdpsettings('solver','daqp');

% Solve problem
sol = optimize(cons,obj,options);