Two interior point continuous trajectory models for convex quadratic programming with bound constraints

In this paper, two interior point continuous trajectory models are introduced for solving convex quadratic programming with bound constraints. The main components of our two interior point continuous trajectory models arc two dynamical systems, one for each model. These two dynamical systems arc very simple, only matrix-vector multiplications arc required. Without introducing dual variables or projection, starting from any interior point, all solution trajectories of our two dynamical systems remain in the interior of the feasible regions and will converge to optimal solutions of the underlying optimization problems in the limit. Many theoretical properties for the two dynamical systems are presented. In particular, in our convergence proofs for the solutions of the two dynamical systems, there is no Lyapunov function involved. Furthermore, our preliminary simulation results are very encouraging in obtaining optimal solutions of the corresponding optimization problems.