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of 485
pro vyhledávání: '"49N15"'
This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum of the corr
Externí odkaz:
http://arxiv.org/abs/2410.01436
Autor:
Jeong, Seonghyeon
Optimal transportation problem seeks for a coupling $\pi$ of two probability measures $\mu$ and $\nu$ which minimize the total cost $\int c d\pi$, which is linear in $\pi$. In this paper, we introduce a variation of optimal transportation problem whi
Externí odkaz:
http://arxiv.org/abs/2408.05161
Autor:
Kostyukova, O. I.
For a proper cone $K$ and its dual cone $K^*$ in $\mathbb R^n$, the complementarity set of $K$ is defined as ${\mathbb C}(K)=\{(x,y): x\in K,\; y\in K^*,\, x^\top y=0\}$. It is known that ${\mathbb C}(K)$ is an $n$-dimensional manifold in the space $
Externí odkaz:
http://arxiv.org/abs/2404.17375
In this paper, we investigate Monge-Kantorovich problems for which the absolute continuity of marginals is relaxed. For $X,Y\subseteq\mathbb{R}^{n+1}$ let $(X,\mathcal{B}_X,\mu)$ and $(Y,\mathcal{B}_Y,\nu)$ be two Borel probability spaces, $c:X\times
Externí odkaz:
http://arxiv.org/abs/2404.13616
Autor:
Ciosmak, Krzysztof Jan
In [K.J. Ciosmak, Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions, Nonlinear Anal. 232 (2023), Paper No. 113267, 32 pp.], Theorem 2.3. does not suffi
Externí odkaz:
http://arxiv.org/abs/2404.10797
Autor:
Backus, Aidan
Motivated by Thurston and Daskalopoulos--Uhlenbeck's approach to Teichm\"uller theory, we study the behavior of $q$-harmonic functions and their $p$-harmonic conjugates in the limit as $q \to 1$, where $1/p + 1/q = 1$. The $1$-Laplacian is already kn
Externí odkaz:
http://arxiv.org/abs/2404.02215
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two marginal problem
Externí odkaz:
http://arxiv.org/abs/2403.20238
Autor:
Fajardo, M. D., Vidal-Nunez, J.
In this paper we study how Lagrange duality is connected to optimization problems whose objective function is the difference of two convex functions, briefly called DC problems. We present two Lagrange dual problems, each of them obtained via a diffe
Externí odkaz:
http://arxiv.org/abs/2403.11248
In this paper we investigate how the subgradients of the value function of a discrete-time convex Bolza problem evolve over time. In particular, we develop a discrete-time version of the characteristic method introduced by Rockafellar and Wolenski in
Externí odkaz:
http://arxiv.org/abs/2402.00289
We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum of all Gatzouras-Lalley carpets as the concave conjugate of an explicit
Externí odkaz:
http://arxiv.org/abs/2401.07168