Hybrid Robust Optimal Resource Allocation with Momentum

We study the problem of robust resource allocation with momentum following a dynamical systems point of view. Motivated by a class of existing optimization dynamics with no momentum defined on the general m-simplex, we propose a class of time-varying differential equations with momentum that achieve...

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Bibliographic Details
Main Authors: Ochoa, Daniel E., Poveda, Jorge I., Uribe, Cesar A., Quijano, Nicanor
Format: Conference Proceeding
Language:English
Subjects:
Acceleration
Asymptotic stability
Cost function
Mathematical model
Resource management
Robustness
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Summary:We study the problem of robust resource allocation with momentum following a dynamical systems point of view. Motivated by a class of existing optimization dynamics with no momentum defined on the general m-simplex, we propose a class of time-varying differential equations with momentum that achieve acceleration and preserve most of the asymptotic properties of its time-invariant counterpart. Since time-varying dynamics with momentum in continuous-time usually lack of structural robustness properties, we present a hybrid regularization that induces the property of uniform asymptotic stability in the system. We show this by using the invariance principle for well-posed hybrid dynamical systems, and we establish the existence of strictly positive margins of robustness with respect to arbitrarily small disturbances. We illustrate our results via numerical simulations.
ISSN:2576-2370
DOI:10.1109/CDC40024.2019.9028936