Determining functions by slopes
L Thibault, D Zagrodny - Communications in Contemporary …, 2023 - World Scientific
Determining functions by slopes Page 1 Communications in Contemporary Mathematics Vol.
25, No. 7 (2023) 2250014 (30 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219199722500146 …
25, No. 7 (2023) 2250014 (30 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219199722500146 …
Metric compatibility and determination in complete metric spaces
A Daniilidis, TM Le, D Salas - Mathematische Zeitschrift, 2024 - Springer
The local slope operator was introduced in De Giorgi et al.(Atti Accad Naz Lincei Rend Cl
Sci Fis Mat Nat 68: 180–187, 1980) to study gradient flow dynamics in metric spaces. This …
Sci Fis Mat Nat 68: 180–187, 1980) to study gradient flow dynamics in metric spaces. This …
[HTML][HTML] Descent modulus and applications
The norm of the gradient‖∇ f (x)‖ measures the maximum descent of a real-valued
smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance …
smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance …
Well-posedness of fractional Moreau's sweeping processes of Caputo type
In this paper, we study the well-posedness (in the sense of existence and uniqueness of a
solution) of a sweeping process involving fractional order derivative of Caputo type in Hilbert …
solution) of a sweeping process involving fractional order derivative of Caputo type in Hilbert …
A slope generalization of Attouch theorem
A Daniilidis, D Salas, S Tapia-García - Mathematical Programming, 2024 - Springer
A classical result of variational analysis, known as Attouch theorem, establishes an
equivalence between epigraphical convergence of a sequence of proper convex lower …
equivalence between epigraphical convergence of a sequence of proper convex lower …
The slope robustly determines convex functions
A Daniilidis, D Drusvyatskiy - Proceedings of the American Mathematical …, 2023 - ams.org
We show that the deviation between the slopes of two convex functions controls the
deviation between the functions themselves. This result reveals that the slope—a one …
deviation between the functions themselves. This result reveals that the slope—a one …
Moreau envelope of supremum functions with applications to infinite and stochastic programming
P Pérez-Aros, E Vilches - SIAM Journal on Optimization, 2021 - SIAM
In this paper, we investigate the Moreau envelope of the supremum of a family of convex,
proper, and lower semicontinuous functions. Under mild assumptions, we prove that the …
proper, and lower semicontinuous functions. Under mild assumptions, we prove that the …
[PDF][PDF] Slopes and Moreau-Rockafellar Theorem
arXiv:2309.03505v1 [math.FA] 7 Sep 2023 Slopes and Moreau-Rockafellar Theorem Page 1
arXiv:2309.03505v1 [math.FA] 7 Sep 2023 Slopes and Moreau-Rockafellar Theorem M …
arXiv:2309.03505v1 [math.FA] 7 Sep 2023 Slopes and Moreau-Rockafellar Theorem M …
On (discounted) global Eikonal equations in metric spaces
TM Lê, S Tapia-García - arXiv preprint arXiv:2410.00530, 2024 - arxiv.org
Eikonal equations in metric spaces have strong connections with the local slope operator (or
the De Giorgi slope). In this manuscript, we explore and delve into an analogous model …
the De Giorgi slope). In this manuscript, we explore and delve into an analogous model …
[PDF][PDF] Determination of functions by metric slopes
A Daniilidis, D Salas - arXiv preprint arXiv:2109.13721, 2021 - arxiv.org
arXiv:2109.13721v1 [math.OC] 28 Sep 2021 Page 1 Determination of functions by metric
slopes Aris Daniilidis, David Salas Abstract. We show that in a metric space, any continuous …
slopes Aris Daniilidis, David Salas Abstract. We show that in a metric space, any continuous …