Strong and Weak Convexity of Sets and Functions

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Frank-Wolfe Algorithms for Saddle Point Problems (2016, background): “One can (roughly) deﬁne strongly convex sets as sublevel sets of strongly convex functions (Vial, 1983, Prop.”
Approximate convexity and submonotonicity (2004, background): “Moreover, every such function is characterized by its (locally) decomposability as a sum of a convex continuous and a concave quadratic function, see [ 24 ] e.g.”
Iteration complexity of feasible descent methods for convex optimization (2014, background): “The strong convexity in Assumption 2.1 implies that the sublevel set is bounded (Vial, 1983).”
Discontinuous sweeping process with prox-regular sets (2017, methodology): “1 are general and different from those of the aforementioned results in [34, 35].”
Projection-Free Optimization on Uniformly Convex Sets (2020, background): “…projection-free algorithm that has a regret of O ( T 2 / 3 ) with high probability improving over the deterministic O ( T 3 / 4 ) of (Hazan and Kale, 2012) and Levy and Krause (2019) designed a projection-free online algorithm over smooth decision sets; dual to uniformly convex sets (Vial, 1983).”
Subsmooth sets: Functional characterizations and related concepts (2004, background): “This class of functions, initially introduced by Vial [ 33 ], has been extensively used by many authors under various equivalent deflnitions (see [15] and references therein) and enjoys various interesting properties.”