An Accelerated Interior-Point Method for Convex Optimization Leveraging Backtracking Mitigation

Backtracking is generally used for interior-point methods (IPMs) to keep some optimization parameters within a defined boundary. The idea is to reduce the step size such that the optimality conditions are fulfilled. However, backtracking might impede progress toward the optimal point, requiring longer solving time and higher iteration numbers, which are undesirable in real-time applications. In this paper, we present a novel algorithm based on an interior-point method that, in addition to accepting infeasible start guess points, liberates the Lagrange multiplier associated with the inequality constraints from backtracking. Accordingly, a new strategy for updating the weighting factor of the barrier function is proposed. The performance of this new IPM is benchmarked with well-known optimization solvers for solving both linearly and quadratically constrained quadratic programming (QP) problems, which are formulated based on an application of model predictive control (MPC) in the automotive industry. Furthermore, the new IPM has been implemented on embedded hardware and validated in an experimental real vehicle. The testing results show that the new IPM takes considerably fewer iterations and computational time to solve QP problems than other tested solvers.