Trajectory convergence from coordinate-wise decrease of general convex energy functions

Julien, M. Hendrickx and Gerencsér, Balázs (2022) Trajectory convergence from coordinate-wise decrease of general convex energy functions. AUTOMATICA, beküld. ISSN 0005-1098

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Abstract

We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some convex energy function. We show that this simple condition guarantees convergence to a point, to the minimum of the energy functions, or to a set where its Hessian has very specific properties. This extends and strengthens recent results that were restricted to quadratic energy functions.

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