An efficient quadratic programming implementation for cross directional control of large papermaking processes

In this paper, we consider a linearly constrained quadratic programming (QP) problem arising from cross directional control of large papermaking processes. Different from general-purpose QP solvers, we solve the optimization problem by taking advantage of the problem structure and features, such as positive-definiteness of the Hessian matrix, sparsity of the Hessian and constraint matrices. It is implemented based on a dual feasible, active-set algorithm, a Schur complement method and a warm start strategy. The Schur complement is proved to be nonsingular throughout iterations, which makes the solver numerically very reliable. In comparison with the standard Matlab QP solver, the proposed QP solver is much more efficient in the case studies we performed on real industrial papermaking processes.