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23.2 Quadratic Programming

Octave can also solve Quadratic Programming problems, this is

min 0.5 x'*H*x + x'*q

subject to

A*x = b
lb <= x <= ub
A_lb <= A_in*x <= A_ub

Function File: [x, obj, info, lambda] = qp (x0, H, q, A, b, lb, ub, A_lb, A_in, A_ub)

Solve the quadratic program

min 0.5 x'*H*x + x'*q
 x

subject to

A*x = b
lb <= x <= ub
A_lb <= A_in*x <= A_ub

using a null-space active-set method.

Any bound (A, b, lb, ub, A_lb, A_ub) may be set to the empty matrix ([]) if not present. If the initial guess is feasible the algorithm is faster.

The value info is a structure with the following fields:

solveiter

The number of iterations required to find the solution.

info

An integer indicating the status of the solution, as follows:

0

The problem is feasible and convex. Global solution found.

1

The problem is not convex. Local solution found.

2

The problem is not convex and unbounded.

3

Maximum number of iterations reached.

6

The problem is infeasible.