Related papers: Spectrally Optimized Pointset Configurations
We study the secure stochastic convex optimization problem. A learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle. In the meantime, there exists an adversary who aims to…
The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…
Tutte's spring embedding theorem states that, for a three-connected planar graph, if the outer face of the graph is fixed as the complement of some convex region in the plane, and all other vertices are placed at the mass center of their…
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
In this paper we study the asymptotic properties of point configurations that achieve optimal covering of sets lacking smoothness. Our results include the proofs of the existence of asymptotics of best covering and maximal polarization for…
We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduce an appropriate weak formulation in fractional Sobolev…
We begin by revisiting a paper of Erd\H{o}s and Fishburn, which posed the following question: given $k\in \mathbb{N}$, what is the maximum number of points in a plane that determine at most $k$ distinct distances, and can such optimal…
We establish a maximum principle for a two-point function in order to analyze the convexity of level sets of harmonic functions. We show that this can be used to prove a strict convexity result involving the smallest principal curvature of…
In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making,…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…
We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they may fail with a certain failure rate. The goal is to find the optimal locations as well as the…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…
We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms…
For configurations of point-sets that are pairwise constrained by distance intervals, the EASAL software implements a suite of algorithms that characterize the structure and geometric properties of the configuration space. The algorithms…
In the Seat Arrangement problem the goal is to allocate agents to vertices in a graph such that the resulting arrangement is optimal or fair in some way. Examples include an arrangement that maximises utility or one where no agent envies…