Gradient descent with step size alpha in (0, 2/L) globally converges for functions with sector-bounded gradients, proved through a discrete-time passivity argument, with a boundary case treated via the weak passivity theorem.
Global Convergence and Asymptotic Optimality of the Heavy Ball Method for a Class of Nonconvex Optimization Problems,
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Input-Output Stability of Gradient Descent: A Discrete-Time Passivity-Based Approach
Gradient descent with step size alpha in (0, 2/L) globally converges for functions with sector-bounded gradients, proved through a discrete-time passivity argument, with a boundary case treated via the weak passivity theorem.