5 papers
Sharp inequalities between Zolotarev and Wasserstein distances in
Karol BoÅbotowski, Guy Bouchitté
Based on a new Kantorovich-Rubinstein duality principle for the Hessian that was recently established by the two authors, we extend the Rio inequality to any dimension wi…
Bi-martingale optimal transport and its applications
Karol BoÅbotowski
We introduce a new non-linear optimal transport formulation for a pair of probability measures on sharing a common barycentre, in which admissible transference plans…
Kantorovich-Rubinstein duality theory for the Hessian
Karol BoÅbotowski, Guy Bouchitté
The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschit…
Topology and geometry optimization of grid-shells under self-weight loading
Helen E. Fairclough, Karol Bolbotowski, Linwei He +2
This manuscript presents an approach for simultaneously optimizing the connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) under the co…
The Isotropic Material Design methods with the cost expressed by the -norm
Karol BoÅbotowski, SÅawomir Czarnecki, Tomasz LewiÅski
The paper concerns the problem of minimization of the compliance of linear elastic structures made of an isotropic material. The bulk and shear moduli are the design variables, bot…