Variational Analysis and Generalized Differentiation

By F. Giannessi. 2006

1,260 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/302060358713a4918a6cd979b29a12a0637668e7

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In Control and Systems Engineering

Citations in the corpus

Parabolic regularity in geometric variational analysis (2019, methodology): “, [36, 37, 47] with the commentaries and references therein.”
ABOUT STATIONARITY AND REGULARITY IN VARIATIONAL ANALYSIS (2009, methodology): “The last 639 inclusion is equivalent (see [29,39]) to x∗ ∈ ∂f(x̄).”
Second-order growth, tilt stability, and metric regularity of the subdifferential (2013, background): “We refer the reader to [17, 26] for the latter subdifferential construction and to [26] for properties and applications of fully amenable functions.”
From error bounds to the complexity of first-order descent methods for convex functions (2015, methodology): “1 Some convex analysis We use the standard notation from [60] (see also [7, 58] and [52]).”
Exact penalty results for mathematical programs with vanishing constraints (2010, background): “The Fréchet normal cone is sometimes also called the regular normal cone, most notably in [21], whereas the limiting normal cone comes with a number of different names, including normal cone, basic normal cone, and Mordukhovich normal cone due to the many contributions of Mordukhovich in this area, ”
Linear convergence of the Douglas–Rachford method for two closed sets (2014, methodology): “The notation used in this paper is quite standard and follows primarily [9, 29, 31].”
Openness stability and implicit multifunction theorems: Applications to variational systems (2011, methodology): “We begin our analysis with an interesting result due to Ursescu (see, e.g., [12, Theorem 1]), which brings into the light the key fact that the linear openness property of a difference type multifunction can be deduced from the corresponding linear openness properties of its terms.”
Approximation and optimization of discrete and differential inclusions described by inequality constraints (2011, neutral): “An important role of this method both from the theoretical and practical points of view are demonstrated in Mahmudov [5–11] and Mordukhovich [16].”
On the theory of subdifferentials (2012, background): “By now there are several more versions of the theorem [40, 54, 58].”
METRIC REGULARITY—A SURVEY PART 1. THEORY (2016, methodology): “There are a number of monographs and survey articles in which subdifferentials are studied at various levels of generality: [91] (finite-dimensional theory), [17, 77, 85, 94] (Asplund spaces), [57, 85] (general Banach spaces), [22, 23] (generalized gradients).”
Error Bounds and Hölder Metric Subregularity (2014, background): “, [5,36] for discussions and characterizations of Asplund spaces.”
Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications (2008, background): “The Fréchet normal cone is sometimes also called the regular normal cone, most notably in [33], whereas the limiting normal cone comes with a number of different names, including normal cone, basic normal cone, and Mordukhovich normal cone due to the many contributions of Mordukhovich in this area, ”
OPTIMAL CONTROL OF THE SWEEPING PROCESS (2012, methodology): “To the best of our knowledge, the strong approximation type obtained for general differential inclusions (see [5, 11, 13] and the references therein) cannot be applied to the sweeping system under consideration since the Lipschitz continuity assumption of [11, 13] and the “modified one-sided Lipschi”
Nonsmooth analysis of doubly nonlinear evolution equations (2011, neutral): “[39, 40], and [44, 45, 46] for some analysis of gradient flow and doubly nonlinear equations featuring such a notion of subdifferential), defined by ∂limEt(u) := {ξ ∈ R : ∃ (un), (ξn) ⊂ R, un → u, ξn → ξ, Et(un) → Et(u)}.”
Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces (2007, methodology): “Moreover, the latter property is satisfied far beyond convexity; see a number of sufficient conditions for it in [16, 17, 20] and the references”
Clarke Subgradients of Stratifiable Functions (2006, methodology): “For nonsmooth analysis we refer to the comprehensive texts [5], [6], [28], [29], [32].”