OQLA/QPALM – Convex quadratic optimization solvers using the augmented Lagrangian approach, with an appropriate behavior on infeasible or unbounded problems

When a solver of convex quadratic optimization problem (QP) is used within a nonlin-ear optimization code, implementing the SQP algorithm, it is important that it deals appropriately with the special QPs that can be generated by the nonlinear solver, those that are infeasible or unbounded. The goal of this paper is to highlight the po-tential of the augmented Lagrangian (AL) algorithm in that respect and to give an account on the efficiency of the implementation of this algorithm in the C++/Matlab codes Oqla/Qpalm. We show how these pieces of software compare with some fre-quently used QP solvers, which use active-set or interior-point methods, and demon-strate that they provide an appropriate response when they deal with the special QPs quoted above.