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Optimization and nonsmooth analysis
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TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
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Journal ArticleDOI
An open mapping principle for set-valued maps
TL;DR: In this paper, the authors prove an open mapping principle for set-valued maps on Banach spaces using kth order variations, which is similar to the one we consider in this paper.
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A class of fractional differential hemivariational inequalities with application to contact problem
TL;DR: In this paper, a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces is studied, where the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient are used to establish existence of solution to the abstract inequality.
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Metric Inequality, Subdifferential Calculus and Applications
Huynh Van Ngai,Michel Théra +1 more
TL;DR: In this article, the authors established characterizations of Asplund spaces in terms of conditions ensuring the metric inequality and intersection formulae, and established chain rules for the limiting Frechet subdifferentials.
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Generalized convexity of functions and generalized monotonicity of set-valued maps
J.-P. Penot,P. H. Quang +1 more
TL;DR: In this paper, it was shown that if a function f is continuous, then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar.
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A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems
Alexander Mielke,Michael Ortiz +1 more
TL;DR: In this article, the Euler-Lagrange equation is replaced by a weighted dissipation-energy functional with a weight decaying with a rate 1/�, which is defined by a sequence of time-discretized minimum problems and formally passing to the limit of continuous time.