A unified framework using scaled Kurdyka-Lojasiewicz inequalities shows that Bregman proximal point and gradient methods, and mirror flow, converge for closed-domain separable kernels and subanalytic or definable objectives.
Convergence of the iterates of descent methods for analytic cost functions.SIAM Journal on Optimization, 16(2): 531–547, 2005
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A Unified Framework for Iterate Convergence of Bregman Proximal Methods
A unified framework using scaled Kurdyka-Lojasiewicz inequalities shows that Bregman proximal point and gradient methods, and mirror flow, converge for closed-domain separable kernels and subanalytic or definable objectives.