Author

Kim-Chuan Toh

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Preprint Aug 2026

Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization

Sequence convergence to a boundary Karush--Kuhn--Tucker (KKT) point has long remained unclear for nonconvex mirror descent with Legendre kernels. The difficulty arises from the blow-up of the gradient of the Legendre kernel at the boundary. Recent work~\cite{dingtoh2026nonkkt} shows that mirror descent can accumulate a...

Kuangyu Ding, Kim-Chuan Toh · 0 citations

#machine learning Preprint Aug 2026

Non-KKT Accumulation in Entropic Mirror Descent

For mirror descent generated by a Legendre kernel, perhaps one of the most basic question in optimization is this: must every accumulation point of a bounded mirror descent sequence be Karush--Kuhn--Tucker (KKT) stationary under proper stepsizes? We show that the answer is no. A longstanding obstacle to resolving this...

Kuangyu Ding, Kim-Chuan Toh · 1 citation