基于鲁棒控制的自适应分数阶梯度优化算法设计OA北大核心CSTPCD

The vanilla fractional order gradient descent may converge to a region around the global minimum instead of converging to the exact minimum point,or even diverge,in the case where the objective function is strongly convex.To address this problem,a novel adaptive fractional order gradient descent(AFOGD)method and a novel adaptive fractional order accelerated gradient descent(AFOAGD)method are proposed in this paper.Inspired by the quadratic constraints and Lyapunov stability analysis from robust control theory,we establish a linear matrix inequality to analyse the convergence of our proposed algorithms.We prove that our proposed algorithms can achieve R-l inear convergence when the objective function is L-smooth and m-strongly-convex.Several numerical simulations are demonstrated to verify the effectiveness and superiority of our proposed algorithms.