Setting up the problem

In C we define the problem as

// Define the problem
int n = 2; // Number of decision variables
int m = 4; // Number of constraints (general + simple)
int ms= 2; // Number of simple bounds
double H[4] = {1, 0, 0, 1};
double f[2] = {1,1}; 
double A[4] = {1, 2, 1, -1};
double bupper[4] = {1, 2, 3, 4};
double blower[4] = {-1, -2, -3, -4};
int sense[4] = {0,0,0,0}; // Only inequality constraints
DAQPProblem qp = {n,m,ms,H,f,A,bupper,blower,sense};

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

A high-level function daqp_quadprog can be used to solve the problem.

double x[2],lam[4];
DAQPResult result;
result.x = x; // primal variable
result.lam = lam; // dual variable
daqp_quadprog(&result,&qp,NULL);

The last argument is a pointer to a DAQPSettings struct, but passing a null-pointer will result in the default settings being used. The first argument is a pointer to a DAQPResults struct in which solution information will be populated.

The optimal solution can be found in result.x, the optimal function value in result.fval, and the exit flag in result.exitflag. The struct result also contains some profiling information such as solve time and number of iterations.

Changing settings

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

DAQPSettings settings;
daqp_default_settings(&settings); // Populate settings with default values
settings.iter_limit = 2000;

A full list of available settings is provided here.