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We provide a new version of the Tikhonov theorem for both two-scale forward systems and also two-scale forward-backward systems of stochastic differential equations, which also covers the McKean-Vlasov case. Differently from what is usually…
We present a dynamical version for the multi-marginal optimal transport problem with infimal convolution cost, using the theory of Wasserstein barycentres. We show, how our formulation relates to the dynamical version of the multi-marginal…
A general method to describe stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems. The determination of an optimal coordinate for the description of stochastic dynamics. The reconstruction of…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less…
We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
Understanding how complex systems transition between states requires mapping the energy landscape that governs these changes. Local transition-state networks reveal the barrier architecture that explains observed behaviour and enables…
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…
We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it…
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently…
In this manuscript we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the second order in time dynamics, combining viscous and Hessian-driven damping with a…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…
This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…