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Weaker conditions for subdifferential calculus of convex functions
(Elsevier, 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 ...
Synergistic solutions for merging and computing planar convex hulls
(Springer Verlag, 2018)
We describe and analyze the first adaptive algorithm for merging k convex hulls in the plane. This merging algorithm in turn yields a synergistic algorithm to compute the convex hull of a set of planar points, taking ...
On the klee-saint raymond's characterization of convexity
(SIAM, 2016)
Using techniques of convex analysis, we provide a direct proof of a recent characterization of convexity given in the setting of Banach spaces in [J. Saint Raymond, J. Nonlinear Convex Anal., 14 (2013), pp. 253-262]. Our ...
Weak compactness of sublevel sets in complete locally convex spaces
(Heldermann Verlag, 2019)
© 2019 Heldermann Verlag. All rights reserved.In this work we prove that if X is a complete locally convex space and {equation presented} is a function such that f -x∗attains its minimum for every x∗∈ U, where U is an open ...
Characterizations of the subdifferential of convex integral functions under qualification conditions
(Academic Press Inc., 2019)
This work provides formulae for the ε-subdifferential of integral functions in the framework of complete σ-finite measure spaces and locally convex spaces. In this work we present here new formulae for this ε-subdifferential ...
Critical angles between two convex cones I. General theory
(Springer, 2016)
The concept of critical (or principal) angle between two linear subspaces has applications in statistics, numerical linear algebra, and other areas. Such concept has been abundantly studied in the literature, both from a ...
Integration of Nonconvex Epi-Pointed Functions in Locally Convex Spaces
(Hekdermann, 2016)
We extend the results of Correa, Garcia and Hantoute [6], dealing with the integration of nonconvex epi-pointed functions using the Fenchel subdifferential. In this line, we prove that the classical formula of Rockafellar ...
Unbounded state-dependent sweeping processes with perturbations in uniformly convex and q-uniformly smooth banach spaces
(Amer INST. mathematical sciences-AIMS, 2018-03)
In this paper, the existence of solutions for a class of first and second order unbounded state-dependent sweeping processes with perturbation in uniformly convex and q-uniformly smooth Banach spaces are analyzed by using ...
Inner estimation of the eigenvalue set and exponential series solutions to differential inclusions
(HELDERMANN VERLAG, 2005-11-01)
We obtain inner estimations, around special eigenvalues, for the eigenvalue set of a properly nonlinear closed convex process. We also consider a differential inclusion associated with a general closed convex process and ...
Valadier-like formulas for the supremum function I
(Heldermann Verlag, 2018)
We generalize and improve the original characterization given by Valadier [18, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby ...