A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation

Abstract

Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming subproblem is close to the true Hessian. However, a good Hessian approximation can be expensive to compute. Low cost Hessian approximations only guarantee local convergence under some assumptions, which are not always satisfied in practice. To address this problem, this paper proposes a simple method to guarantee local convergence for SQP with poor Hessian approximation. The effectiveness of the proposed algorithm is demonstrated in a numerical example.

Nonlinear Model Predictive Motion Control of Linear Motor Drive for Micro/Nano-Positioning Applications

“…Model predictive control (MPC) which was traditionally designed for slow systems commonly seen in chemical industries has also been employed for linear motors control and this is aided by the development of fast solvers [23], [24] and increased computational power of computers. In [1], linear MPC was proposed for the tracking of piecewise constant references by a linear motor.…”