Results 11 to 20 of about 425 (153)
Nonsmooth analysis: differential calculus of nondifferentiable mappings [PDF]
Transactions of the American Mathematical Society, 1981 A new approach to local analysis of nonsmooth mappings from one Banach space into another is suggested. The approach is essentially based on the use of set-valued mappings of a special kind, called fans, for local approximation. Convex sets of linear operators provide an example of fans.
A. D. Ioffe
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Convex subcones of the contingent cone in nonsmooth calculus and optimization [PDF]
Transactions of the American Mathematical Society, 1987 The tangential approximants most useful in nonsmooth analysis and optimization are those which lie "between" the Clarke tangent cone and the Bouligand contigent cone. A study of this class of tangent cones is undertaken here. It is shown that although no convex subcone of the contingent cone has the isotonicity property of the contingent cone, there ...
Doug Ward
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Nonsmooth Problems of Calculus of VariationsviaCodifferentiation [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2014 In this paper multidimensional nonsmooth, nonconvex problems of the calculus of variations with codifferentiable integrand are studied. Special classes of codifferentiable functions, that play an important role in the calculus of variations, are introduced and studied.
Maxim Dolgopolik, Dolgopolik, Maxim
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Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations [PDF]
Communications on Pure and Applied Analysis, 2003 Paper accepted for the invited session on "Optimal Control" of the 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control, Sevilla, Spain, April 3-5, 2003.
Torres, D.F.M.
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Nonsmooth implicit differentiation for machine learning and optimization [PDF]
, 2021 In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a nonsmooth form of ...
Bolte, Jérôme +3 more
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Nonsmooth nonconvex stochastic heavy ball [PDF]
, 2023 Motivated by the conspicuous use of momentum-based algorithms in deep learning, we study a nonsmooth nonconvex stochastic heavy ball method and show its convergence. Our approach builds upon semialgebraic (definable) assumptions commonly met in practical
Le, Tam
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Variational Methods for Nonsmooth Mechanics [PDF]
, 2003 In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods.
Fetecau, Razvan Constantin
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KKT reformulation and necessary conditions for optimality in nonsmooth bilevel optimization [PDF]
, 2014 For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question.
Zemkoho, Alain B., Dempe, Stephan
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Discrete Exterior Calculus [PDF]
, 2003 This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complex and its geometric dual.
Hirani, Anil Nirmal
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Nonsmooth pseudodifferential boundary value problems on manifolds [PDF]
, 2019 We study pseudodifferential boundary value problems in the context of the Boutet de Monvel calculus or Green operators, with nonsmooth coefficients on smooth compact manifolds with boundary. In order to have a definition that is independent of the choice
Jiménez, Carolina Neira, Abels, Helmut
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