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 at non-KKT boundary points despite decreasing objective values, precluding a convergence guarantee to KKT points in general. Despite this negative result, mirror descent remains effective in many real applications. Motivated by this contrast, we address the boundary difficulty directly and establish KKT convergence of mirror descent for a broad class of structured nonconvex p...
| Authors | Kuangyu Ding, Kim-Chuan Toh |
|---|---|
| Primary category | math.OC |
| Published | 7 August 2026 |
| Last updated at source | 28 August 2026 |
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