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Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
The ultraslow dynamics of glass-formers has been explained by two views considered as mutually exclusive: one invokes locally hindered mobility, the other rests on the complexity of the configuration space. Here we demonstrate that the…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
We perform exact diagonalization and time evolution of the Lechner-Hauke-Zoller (LHZ) annealing architecture [Science Advances 1(9), e1500838 (2015)] for ten physical qubits. Thereby, on a training set consisting of $2400$ problem…
We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
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…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
Classification trees continue to be widely adopted in machine learning applications due to their inherently interpretable nature and scalability. We propose a rolling subtree lookahead algorithm that combines the relative scalability of the…
In this paper we provide a rigorous convergence analysis for the renowned particle swarm optimization method by using tools from stochastic calculus and the analysis of partial differential equations. Based on a time-continuous formulation…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The aim of this work is to prove that it is possible to realise an optical system which produces as output a light intensity that can be expressed in the same mathematical form of the spin glass Hamiltonian. The optical system under study…
We consider $h$-stable local optima of Ising spin glass models, defined as spin configurations such that for nearly all of the spins, flipping their values results in increasing energy by at least a given amount $h$. Spins satisfying this…
Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important…
Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of…
Our goal is to discuss in detail the calculation of the mean number of stationary points and minima for random isotropic Gaussian fields on a sphere as well as for stationary Gaussian random fields in a background parabolic confinement.…
We propose a numerical algorithm for computing approximately optimal solutions of the matching for teams problem. Our algorithm is efficient for problems involving large number of agent categories and allows for non-discrete agent type…
We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…