Kurdyka–?ojasiewicz Exponent via Inf-projection

Kurdyka–?ojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL $$\frac{1}{2}$$ for suitable potential function is related to local linear convergence. Nevertheless, general extremely hard estimate. this paper, we show under mild assumptions that preserved via inf-projection. Inf-projection fundamental operation ubiquitous when reformulating optimization problems lift-and-project approach. By studying its on exponent, several convex models, including some semidefinite-programming-representable functions and involve $$C^2$$ -cone reducible structures, conditions such as strict complementarity. Our results are applicable concrete models group-fused Lasso overlapping group Lasso. addition, nonconvex difference-of-convex can be derived from their natural majorant functions, Bregman envelope same itself. Finally, estimate sum least squares indicator set matrices rank at most k.