Related papers: Spectrally Optimized Pointset Configurations
We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…
We study the optimal control problem for a control-affine system, where we want to minimize the $L^1$ norm of the control. First, we show how Pontryagin Maximum Principle (PMP) applies to this problem and we divide the extremal trajectories…
In this paper, an optimal consensus problem with local inequality constraints is studied for a network of single-integrator agents. The goal is that a group of single-integrator a gents rendezvous at the optimal point of the sum of local…
We observe natural exceptional points in the excitation spectrum of an exciton-polariton system by optically tuning the light-matter interactions. The observed exceptional points do not require any spatial or polarization degrees of freedom…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
In discrete choice experiments, the information matrix depends on the model parameters. Therefore designing optimally informative experiments for arbitrary initial parameters often yields highly nonlinear optimization problems and makes…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of…
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
For $t \in [-1, 1)$, a set of points on the $(n-1)$-dimensional unit sphere is called $t$-almost equiangular if among any three distinct points there is a pair with inner product $t$. We propose a semidefinite programming upper bound for…
A graph $G$ is a \emph{max point-tolerance (MPT)} graph if each vertex $v$ of $G$ can be mapped to a \emph{pointed-interval} $(I_v, p_v)$ where $I_v$ is an interval of $\mathbb{R}$ and $p_v \in I_v$ such that $uv$ is an edge of $G$ iff $I_u…
We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifold of datasets. Our theory provides theoretical guarantees and explicit bounds on the functional forms of the graph Laplacian when it…
For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution. Even when an optimal regularisation technique is used,…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…
We introduce and study Laplacians on a finite metric graph endowed with generalized densities, that is, measures of finite mass. One important motivation is that this setting provides a common framework for several interesting classes of…
We discuss the design of interlayer edges in a multiplex network, under a limited budget, with the goal of improving its overall performance. We analyze the following three problems separately; first, we maximize the smallest nonzero…