Identifying active constraints via partial smoothness and prox-regularity

By W. Hare, A. S. Lewis. 2003

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Distributed Learning with Sparse Communications by Identification (2018, background): “with identi˙cation properties. Identi˙cation of optimal structure has been extensively studied in the context of constrained convex optimization (e.g. [69]) and nonsmooth nonconvex optimization (e.g. [19]). Although many deterministic algorithms have been proved to have identi˙cation properties, the”
Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods (2016, background): “6 Following [18], this notion means that locally M can be expressed as the solution set of a collection of C2 equations with linearly independent gradients.”
Asynchronous Distributed Learning with Sparse Communications and Identification (2018, background): “Identiﬁcation of optimal structure has been studied for a long time in the context of constrained convex optimization (see e.g. [34]) and nonsmooth nonconvex optimization (e.g. [9]).”
Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence (2017, methodology): “This idea of identifying a smooth “manifold” containing the solution x∗ has been generalized to allow polyhedral constraints [10], general convex constraints [94], and even non-convex constraints [33].”