Results 11 to 20 of about 335 (149)
Geometric approach to convex subdifferential calculus
Optimization, 2015 In this paper, we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning
Mordukhovich, Boris S., Nam, Nguyen Mau
openaire +4 more sources
A useful subdifferential in the Calculus of Variations
Nonlinear AnalysiszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bettiol P., De Marco G., Mariconda C.
core +6 more sources
Subdifferential calculus for convex operators
Journal of Mathematical Analysis and Applications, 1981 AbstractWell-known scalar results on the Subdifferential of composite functions are extended to the framework of ordered topological vector spaces. This is done by using the sandwich theorem for convex operators which is derived from an extension of the Hahn-Banach theorem.
Thera, Michel
openaire +2 more sources
Subdifferential calculus in Asplund generated spaces
Journal of Mathematical Analysis and Applications, 2006 In the paper under review some definitions and results of \textit{B. S. Mordukhovich} and \textit{Y. Shao} [Trans. Am. Math. Soc. 348, 1235--1280 (1996; Zbl 0881.49009)] on subdifferential calculus are extended from Asplund to Asplund generated spaces.
Fabian, M. (Marián) +2 more
openaire +5 more sources
Abstract subdifferential calculus and semi-convex functions [PDF]
, 1997 In this paper the authors follow a path that has become popular recently: to introduce and investigate a notion of abstract subdifferential for lower semi-continuous functions in Banach spaces by requiring the candidate for subdifferential to satisfy a priori given (inspired from subdifferential calculus) properties.
Ivanov, Milen, Zlateva, Nadia
openaire +3 more sources
Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions
SIAM Journal on Optimization, 2016 We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption expressing a natural relationship between the lower semicontinuous envelopes of the data functions in the domain of the sum function. We also provide a new
Rafael Correa +2 more
openaire +4 more sources
Characterizations of convex approximate subdifferential calculus in Banach spaces [PDF]
, 2016 International audienceWe establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding ...
Hantoute, Abderrahim +2 more
core +2 more sources
Weaker conditions for subdifferential calculus of convex functions [PDF]
, 2016 In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level of generality among those leading to the Hiriart ...
López, Marco +5 more
core +1 more source
Enlargements of the Moreau-Rockafellar Subdifferential
, 2021 The Moreau-Rockafellar subdifferential is a highly important notion in convex analysis and optimization theory. But there are many functions which fail to be subdifferentiable at certain points.
Kruger, Alexander, y +3 more
core +1 more source
Sequential ε-Subdifferential Calculus for Scalar and Vector Mappings
, 2017 International audienceIn this paper, several sequential formulae are obtained for the Brøndsted-Rockafellar ε-subdifferential of the sum and the composition of two convex and lower semicontinuous mappings defined in reflexive ...
Huerga, L. +3 more
core +1 more source