Related papers: Minimizers for an aggregation model with attractiv…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…
We investigate the ground states of a free energy functional on sphere. The energy consists of an entropy and a nonlocal interaction term that are in competition with each other, as they favour spreading and aggregation, respectively.…
The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
Consider a collection of particles interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at unit separation. For a range of exponents corresponding to mild…
Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…
We study an isoperimetric problem described by a functional that consists of the standard Gaussian perimeter and the norm of the barycenter. This second term has a repulsive effect, and it is in competition with the perimeter. Because of…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive…
In this paper we describe explicitly the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic.
The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of…
We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by R. Frank and E. Lieb that the ball is the…
Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular interactions in a unified theory. This attempt is not…
We provide new general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. A new direct proof of Almgren's 1968 existence result is presented; namely, we produce from a class of…
In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we establish the existence of infinitely many solutions and of a…
In this paper we investigate a class of variational reaction-diffusion systems with strong competition driven by beyond-pairwise interactions. The model involves $d$ nonnegative components interacting through $k$-wise terms, with $3 \leq k…
The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…
This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on $\mathbb{R}^n$, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral…
We develop a theory describing neutral atoms scattering at low energies in an optical lattice. We show that for a repulsive interaction, as the microscopic scattering length increases, the effective scattering amplitude approaches a…