Metric regularity and subdifferential calculus

By Alexander D. Ioffe. 2000

476 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/608b8512f13696f69847ad06103a545ae447b58d

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Citations in the corpus

On Fréchet Subdifferentials (2003, methodology): “The three properties defined above play a very important role in nonsmooth analysis (see [23,45,64, 65,68,72,77,87]).”
METRIC REGULARITY—A SURVEY PART 1. THEORY (2016, background): “10, let us consider, following the original argument in [54], (x, y, v) sufficiently close to x and y, respectively, and such that y , v ∈ F(x).”
Characterizations of Lojasiewicz inequalities and applications (2008, background): “(Strong slope) Let us recall from [18] (see also [28], [6]) the notion of strong slope defined for every x ∈ dom f as follows:”
A survey on error bounds for lower semicontinuous functions (2003, methodology): “Recently Ioffe in [22], Ng-Zheng in [33] and Wu-Ye in [44–46] furnished some sufficient conditions for a global error bound and Penot gave some results in the quasiconvex case in [37].”
Stability of coincidence points and properties of covering mappings (2009, background): “In this case, Theorem 6 in [3] (on a perturbation) gives an affirmative answer to the question.”
Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity (2009, background): “This fact is strongly connected to famous classical results in this area (see [19, 35, 28, 39] for example) and in particular to the notion of ρ -metric regularity introduced in [28] by A. Ioﬀe.”
Error Bounds and Hölder Metric Subregularity (2014, methodology): “2) Replacing Fréchet subdifferentials with some other (possibly abstract) subdifferentials on the given space satisfying a certain set of natural properties including a kind of (fuzzy or exact) sum rule (trustworthy subdifferentials [23,24]); cf.”
Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods (2016, background): “For a discussion on the role of metric regularity in nonsmooth optimization, see for example [21, 42].”
Vector variational principles for set-valued functions (2011, background): “[43]; see also [19] for a theory of subdifferentials for vector-valued functions).”
Metric regularity and Lipschitzian stability of parametric variational systems (2010, methodology): “In what follows we try to avoid (as in [4, 9, 17] and many other publications) using the "at-point" terminology adopted in [5, 23] for neighborhood properties of type (2.”
Error Bounds: Necessary and Sufficient Conditions (2010, result): “By analogy with the (strong) slope [14] (see also [2, 24])”
Openness stability and implicit multifunction theorems: Applications to variational systems (2011, background): “Note that a more general solution map (see [6], [10]) could be investigated from the point of view of several metric regularity concepts.”
Second-order growth, tilt stability, and metric regularity of the subdifferential (2013, background): “, [11]) as “metric regularity at the point.”
The radius of metric regularity (2002, background): “Again, details can be found in [14] and [25] and the works they cite.”
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality (2008, unknown): “Rockafellar and Wets [42], Ioffe [31]).”
Sufficient Conditions for Error Bounds and Applications (2004, unknown): “For recent surveys on metric regularity, see [5], [6], [ 10 ] and [30].”