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New counterexamples challenge KKT stationarity in mirror descent

By PulseAugur Editorial · [1 sources] ·

Researchers have demonstrated that sequences generated by bounded mirror descent, using a Legendre kernel and specific step sizes, do not always converge to a Karush--Kuhn--Tucker (KKT) stationary point. This finding challenges a fundamental question in optimization regarding the stationary points of such sequences. The study constructs counterexamples for Shannon-entropic mirror descent on the nonnegative orthant and the probability simplex, showing that accumulation points can lie on the boundary and include non-KKT points, even with nonincreasing objective values and entropy-relative smoothness. AI

RANK_REASON The cluster contains an academic paper detailing novel mathematical findings in optimization theory. [lever_c_demoted from research: ic=1 ai=0.4]

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New counterexamples challenge KKT stationarity in mirror descent

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The cluster contains an academic paper detailing novel mathematical findings in optimization theory. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Kuangyu Ding, Kim-Chuan Toh ·

    Non-KKT Accumulation in Entropic Mirror Descent

    arXiv:2608.01658v1 Announce Type: cross Abstract: 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 p…

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