On the Absence of Spurious Local Trajectories in Time-Varying Nonconvex Optimization
نویسندگان
چکیده
In this article, we study the landscape of an online nonconvex optimization problem, for which input data vary over time and solution is a trajectory rather than single point. To understand complexity finding global introduce notion spurious (i.e., nonglobal) local trajectory as generalization to spurious in (time-invariant) optimization. We develop ordinary differential equation (ODE) associated with time-varying nonlinear dynamical system which, at limit, characterizes solutions problem. prove that absence closely related transient behavior developed system. particular, show if problem time-varying, variation may force all ODE trajectories initialized arbitrary minima initial gradually converge trajectory. Jacobian along minimum how its eigenvalues are manipulated by natural consequently trigger escaping poor time.
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ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2023
ISSN: ['0018-9286', '1558-2523', '2334-3303']
DOI: https://doi.org/10.1109/tac.2021.3137147