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We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small volume minimizers are convex and uniformly close to a ball.
Under study are some vector optimization problems over the space of Minkowski balls, i.e., symmetric convex compact subsets in Euclidean space. A typical problem requires to achieve the best result in the presence of conflicting goals;…
We consider Newton's problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that…
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well…
The \emph{sensor placement problem} for stochastic linear inverse problems consists of determining the optimal manner in which sensors can be employed to collect data. Specifically, one wishes to place a limited number of sensors over a…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of…
Since the seminal work of Schoen-Uhlenbeck, many authors have studied properties of harmonic maps satisfying Dirichlet boundary conditions. In this article, we instead investigate regularity and symmetry of $\mathbb{S}^2-$valued minimizing…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
We provide theory for computing the lower semi-continuous convex envelope of functionals of the type f(x) plus an l2 misfit, and discuss applications to various non-convex optimization problems. The latter term is a data fit term whereas f…
Integrated task and motion planning problems describe a multi-modal state space, which is often abstracted as a set of smooth manifolds that are connected via sets of transitions states. One approach to solving such problems is to sample…
Distributing points on a (possibly high-dimensional) sphere with minimal energy is a long-standing problem in and outside the field of mathematics. This paper considers a novel energy function that arises naturally from statistics and…