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 question is the boundary blow-up of the Legendre gradient: it keeps every mirror step in the interior, while at a boundary limit, the inverse entropy metric vanishes on active coordinates and can erase the dual-feasibility in the KKT system. We construct $C^\infty$ objectives and bounded sequences generated by the Shannon-entropic mirror descent on the nonnegative orthant $\...
| Authors | Kuangyu Ding, Kim-Chuan Toh |
|---|---|
| Primary category | math.OC |
| Published | 3 August 2026 |
| Last updated at source | 18 August 2026 |
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