Variational analysis and generalized differentiation

By Boris S. Mordukhovich. 2006

1,196 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5212b71404c7dc3217c9603293f90321e588101a

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In Computational Theory and Mathematics

Citations in the corpus

Optimal Control Involving Sweeping Processes (2018, background): “Instead we refer the reader to, for example, [9, 18] and [24].”
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, ”
Proximal alternating linearized minimization for nonconvex and nonsmooth problems (2013, background): “Let us recall few definitions concerning subdifferential calculus (see, for instance, [27,33]).”
Restricted Normal Cones and the Method of Alternating Projections: Applications (2012, methodology): “, [4], [6], [8], [19], [22], [23], [24].”
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 [10], whereas the limiting normal cone comes with a number of different names, including normal cone, basic normal cone, andMordukhovich normal cone due to the many contributions of Mordukhovich in this area, s”
On the Coderivative of the Projection Operator onto the Second-order Cone (2008, neutral): “Keywords: second-order cone, projection, limiting coderivative, Aubin property”
Characterizations of Lojasiewicz inequalities and applications (2008, background): “Let us first recall the notion of Fr´ echet subdifferential (see [13, 36 ]).”
On directionally dependent subdifferentials (2010, methodology): “1 in [4]).”
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 [55] (see also [6, 53] and [49]).”
On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling (2007, neutral): “In [17], it was proposed to do so by using Mordukhovich’s co-derivative D of multifunctions (see [15]) as a basic tool.”
Restricted Normal Cones and the Method of Alternating Projections: Theory (2012, methodology): ““(iii)⇔(iv)”: Noting that the definition of NA(a) in [15] is the one given in (iv), we see that this equivalence follows from [15, Theorem 1.”