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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