🤖 AI Summary
This work addresses the sensitivity to parameters, poor stability, and low computational efficiency commonly observed in gradient-based optimization algorithms for nonlinear model predictive control (NMPC). To overcome these limitations, the authors propose the Search and Accelerate (SaA) algorithm, which integrates adaptive line search, a trust-region mechanism, and gradient acceleration strategies. Specifically designed for box-constrained optimization problems, SaA requires no prior knowledge of the Lipschitz constant and operates effectively with default parameter settings, ensuring broad applicability. Theoretical analysis establishes its convergence and stability properties, while extensive experiments across 600 benchmark instances demonstrate its superior efficiency and robustness. Notably, SaA significantly reduces the NMPC control update cycle, positioning it as a compelling general-purpose alternative to existing gradient-based optimizers.
📝 Abstract
This paper discusses some aspects related to gradient-based optimization algorithms with special focus on the requirements associated to their use in the implementation of Nonlinear Model Predictive Control. Based on a dedicated discussion, a new algorithm, termed Search and Accelerate (SaA) is proposed that mixes together a novel line search, a trust region mechanism together with an adaptation of the gradient acceleration scheme. A dedicated benchmark involving a set of 600 instances of box constrained optimization problems is designed and used in order to show the algorithm performances which make it a highly competitive general purpose gradient-based alternative for box-constrained optimization problems. An appealing feature of the algorithm is its robustness to the choice of the few parameters involved in its definition making the default values a valid option for any problem without a priori knowledge of the related Lipchitz constant. Moreover, an example of use of the proposed algorithm in NMPC implementation is proposed showing the possibility to reduce the control updating period which might be mandatory in some circumstances.