d = DAQP.Model()

creates an empty optimization model d.

The following functions acts on such models:

• DAQP.setup(d,H,f,A,bupper,blower,sense): setup a QP problem (see DAQP.quadprog for problem details)
• DAQP.solve(d): solve a populated model
• DAQP.update(d,H,f,A,bupper,blower,sense): update an existing model
• dict = DAQP.settings(d): return a Dictionary with the current settings for the model d
• DAQP.settings(d,dict): update the settings for d with the Dictionary dict

xstar, fval, exitflag, info = DAQP.linprog(f,A,bupper)
xstar, fval, exitflag, info = DAQP.linprog(f,A,bupper,blower,sense)

finds the solution xstar to the linear program

min_x	f' x
subject to 
    blower[1:ms]	<= x[1:ms] <= bupper[1:ms]
    blower[ms+1:m]  <= A*x 	   <= bupper[ms+1:m],

where m = length(bupper) and ms = m-size(A,2).

Input

• f - linear term in objective function, n-vector
• A - constraint normals, ((m-ms) x n)-matrix
• bupper - upper bounds for constraints, m-vector
• blower - lower bounds for constraints, m-vector (default: -Inf)
• sense - constraint types, m-vector of Cints (default: 0). Example types:
  • 0 : inequality
  • 5 : equality

Output

• xstar - solution provided by solver
• fval - objective function value for xstar.
• exitflag - flag from solver (>0 success, <0 failure)
• info - tuple containing profiling information from the solver.

Example calls

xstar, fval, exitflag, info = DAQP.quadprog(H,f,A,bupper)
xstar, fval, exitflag, info = DAQP.quadprog(H,f,A,bupper,blower,sense)

finds the solution xstar to the quadratic program

 minimize	   0.5 x' H x + f' x
subject to   blower <= A x <= bupper

If bupper and blower have more elements than rows of A, the first elements are interpreted as simple bounds. For example:

    A = [7.0 8.0]
    blower = [-4.0; -5.0; -6.0]
    bupper = [ 1.0;  2.0;  3.0]

is interpreted as

        -4.0 <= x₁ <= 1.0
        -5.0 <= x₂ <= 2.0
    -6.0 <= 7 x₁ + 8 x₂ <= 3.0

Input

• H - cost matrix
• f - cost vector
• A - linear constraint matrix
• buppe - upper bounds for constraints
• blower - lower bounds for constraints (default: -Inf)
• sense - constraint types, as a vector of Cints (default: 0). Example types:
  • 0 : inequality
  • 1 : active inequality (used as warm start)
  • 5 : equality
  • 8 : soft (allowed to be violated if necessary)
  • 16 : binary (either upper or lower bound should hold with equality)

Output

• xstar - solution
• fval - objective function value for xstar.
• exitflag - flag from solver (>0 success, <0 failure)
• info - tuple containing profiling information from the solver.