Corrigendum to "Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization"

1989 ◽  
Vol 311 (1) ◽  
pp. 429
Author(s):  
Doug Ward
Keyword(s):  
Contingent Cone ◽  
Nonsmooth Calculus

On tangential approximations of the solution set of set-valued inclusions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amos Uderzo
Keyword(s):  
Crucial Role ◽  
Variational Analysis ◽  
Necessary Optimality Conditions ◽  
Solution Set ◽  
Inclusion Problem ◽  
Feasible Region ◽  
Contingent Cone ◽  
Constrained Problems ◽  
Outer Approximations ◽  
Set Valued Mappings

Abstract In the present paper, the problem of estimating the contingent cone to the solution set associated with certain set-valued inclusions is addressed by variational analysis methods and tools. As a main result, inner (resp. outer) approximations, which are expressed in terms of outer (resp. inner) prederivatives of the set-valued term appearing in the inclusion problem, are provided. For the analysis of inner approximations, the evidence arises that the metric increase property for set-valued mappings turns out to play a crucial role. Some of the results obtained in this context are then exploited for formulating necessary optimality conditions for constrained problems, whose feasible region is defined by a set-valued inclusion.

Generalized Euler–Lagrange equation for nonsmooth calculus of variations

2013 ◽  
Vol 75 (1-2) ◽  
pp. 85-100 ◽  
Author(s):  
M. H. Noori Skandari ◽  
A. V. Kamyad ◽  
S. Effati
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Equation ◽  
Nonsmooth Calculus

scholarly journals Nonsmooth Calculus in Finite Dimensions

1987 ◽  
Vol 25 (5) ◽  
pp. 1312-1340 ◽  
Author(s):  
D. E. Ward ◽  
J. M. Borwein
Keyword(s):  
Nonsmooth Calculus

Smooth and Nonsmooth Calculus

2016 ◽  
pp. 409-616
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Nonsmooth Calculus

Smooth and Nonsmooth Calculus

2009 ◽  
pp. 1-61 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Sophia Th. Kyritsi-Yiallourou
Keyword(s):  
Nonsmooth Calculus
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