Related papers: An algorithm for computing Fr\'echet means on the …
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
Satellite mission planning for Earth observation satellites is a combinatorial optimization problem that consists of selecting the optimal subset of imaging requests, subject to constraints, to be fulfilled during an orbit pass of a…
We consider the problem of computing the Fr\'echet distance between two curves for which the exact locations of the vertices are unknown. Each vertex may be placed in a given uncertainty region for that vertex, and the objective is to place…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
We consider a problem in quantum theory that can be formulated as an optimisation problem and present a global optimisation algorithm for solving it, the foundation of which relies in turn on a theorem from quantum theory. To wit, we…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to a class of elliptic partial differential equations. We propose a new caching strategy which leverages the continuity of paths…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…
In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Fr\'echet means are a popular type of average for non-Euclidean datasets, defined as those points which minimise the average squared distance to a set of data points. We consider the behaviour of sample Fr\'echet means on normed spaces…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…