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The vanilla fractional order gradient descent may oscillatively converge to aregion around the global minimum instead of converging to the exact minimumpoint, or even diverge, in the case where the objective function is stronglyconvex. To address this problem, a novel adaptive fractional order gradientdescent (AFOGD) method and a novel adaptive fractional order acceleratedgradient descent (AFOAGD) method are proposed in this paper. Inspired by thequadratic constraints and Lyapunov stability analysis from robust controltheory, we establish a linear matrix inequality to analyse the convergence ofour proposed algorithms. We prove that the proposed algorithms can achieveR-linear convergence when the objective function is $\textbf{L-}$smooth and$\textbf{m-}$strongly-convex. Several numerical simulations are demonstrated toverify the effectiveness and superiority of our proposed algorithms.

The Novel Adaptive Fractional Order Gradient Decent Algorithms Design via Robust Control