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();

Using the daqp object is the recommended approach for embedded or real-time applications because it allocates memory only once during setup and reuses it across all subsequent solve calls — no heap allocations occur during solving.

If the problem data changes between solves (e.g., updated cost vector or bounds in an MPC loop), call setup again on the same object to update the internal workspace:

% Update bounds and re-solve (workspace is reused)
bupper_new = [1; 2; 2; 4];
blower_new = -bupper_new;
d.setup(H, f, A, bupper_new, blower_new, sense);
[x, fval, exitflag, info] = d.solve();

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);