2025/04/08 by Tomoya Kamijima, Kamijima, Tomoya, Naoki Marumo +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Spacecraft Dynamics and Control #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2504.05798
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a simple yet highly accurate prediction-correction algorithm, SHARP, for unconstrained time-varying optimization problems. Its prediction is based on an extrapolation derived from the Lagrange interpolation of past solutions. Since this extrapolation can be computed without Hessian matrices or even gradients, the computational cost is low. To ensure the stability of the prediction, the algorithm includes an acceptance condition that rejects the prediction when the update is excessively large. The proposed method achieves a tracking error of O(hp), where h is the sampling period, assuming that the pth derivative of the target trajectory is bounded and the convergence of the correction step is locally linear. We also prove that the method can track a trajectory of stationary points even if the objective function is non-convex. Numerical experiments demonstrate the high accuracy of the proposed algorithm.