When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization
Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm. We develop contact Hamiltonian systems as a setting where the transfer can be made precise. A contact Hamiltonian $H$ on $J^1(\mathbb{R}^n)$ obeys the intrinsic decay identity $\dot H = -H\,\partial_s H$, so an augmented energy $\mathcal{E}$ built from $H$, together with the conformal rate $\partial_s H$, is a continuous-time rate certificate whenever $\mathcal{E}$ controls the objective gap. Our main theorem states, under three named and independently checkable hypotheses, that an order-$r$ contact splitt...
| Authors | George A Kevrekidis |
|---|---|
| Primary category | math.OC |
| Published | 26 July 2026 |
| Last updated at source | 26 July 2026 |
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