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We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…
Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schroedinger bridges to the case of inertial particles with losses and general, possibly singular diffusion…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $R^n$, with the admissible set indexed by the time parameter. The…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…
In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…
This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic…
There has been recent interest in the relaxational modes of small-scale fully connected systems of aligning self-propelled particles (Spera et al., Phys. Rev. Lett. {\bf 132}: 078301 (2024)). We revisit the classical connection between…
Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the stochastic control problem of…