Related papers: Asymptotics of an optimal compliance-location prob…

This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total…

We investigate minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We give a detailed description of the fine geometry of…

We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…

This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization…

The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…

Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…

We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…

We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…

Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…

We investigate the asymptotic behavior, as $N$ grows, of the largest minimal pairwise distance of $N$ points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal…

We review our recent results on the problem of optimizing Riesz means of Laplace eigenvalues among convex sets of given measure in the regime where the cut-off parameter in the definition of the Riesz means tends to infinity. We show that…

We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain,…

Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges to zero, of the optimal control functional and the optimal…

In this paper we analyse local regularity of time-optimal controls and trajectories for an n-dimensional affine control system with a control parameter, taking values in a k-dimensional closed ball. In the case of k equal to n-1, we give…

We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…

We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…

Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the…

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Given a set $P$ of $n$ planar points, two axes and a real-valued score function $f()$ on subsets of $P$, the Optimal Planar Box problem consists in finding a box (i.e. axis-aligned rectangle) $H$ maximizing $f(H\cap P)$. We consider the…