Variational Analysis and Generalized Differentiation II: Applications

By Boris S. Mordukhovich. 2006

861 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b3212381a1c543e2f940c898fd6af22947c799a7

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Citations in the corpus

Optimality conditions for a controlled sweeping process with applications to the crowd motion model (2015, background): “2) significantly differs from those considered in optimal control theory for differential inclusions as developed in [2, 6, 20, 25] and other publications, since (1.”
Spectral Algorithm for Pseudospectral Methods in Optimal Control (2008, methodology): “Such advancements have brought to the forefront many major questions regarding the practice of optimal control theory that were once only in the realmof theory [19,20].”
New necessary optimality conditions in optimistic bilevel programming (2007, methodology): “The second idea involves the application of the normal cone introduced by Mordukhovich [16] to the graph of the argminimum map defined in (1.1), i.e., computing in fact the coderivative of this set-valued mapping.”
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, ”
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 Involving Sweeping Processes (2018, background): “Also, and with respect to strong convergence of velocities for discrete approximations of optimal solutions, we refer the reader to [19] and [22].”
Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces (2007, methodology): “Wayne State University Mathematics Research Reports Mathematics 1-1-2007 Discrete Approximations, Relaxation, and Optimization of One-Sided Lipschitzian Differential Inclusions in Hilbert Spaces Tzanko Donchev University of Architecture and Civil Engineering, Sofia, Bulgaria, tzankodd@gmail.com Elza”
Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming (2006, background): “Further results for minimizing of difference functions subject to general geometric and operator/functional constraints are obtained in this treatise by combining calculus rules for Fréchet subgradients with a more developed calculus of basic/limiting subgradients by Mordukhovich [5] in the framewo”