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math.OC2026
Convergence of difference inclusions: a diameter criterion and step-size conditions
Lexiao Lai, Mingzhi Song
We study bounded realizations of discrete difference inclusions with set-valued increments and additive errors. Our results have two parts. First, we give a general convergence cri…
math.OC2026
On the diameter of subgradient sequences in o-minimal structures
Lexiao Lai, Mingzhi Song
We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is rela…