Related papers: A geometry-based relaxation algorithm for equilibr…
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility…
By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals.…
In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Tight and efficient neural network bounding is crucial to the scaling of neural network verification systems. Many efficient bounding algorithms have been presented recently, but they are often too loose to verify more challenging…
We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves…
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…
This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
The vertex model is a popular framework for modelling tightly packed biological cells, such as confluent epithelia. Cells are described by convex polygons tiling the plane and their equilibrium is found by minimizing a global mechanical…
In this paper, we perform theoretical analyses on the behaviour of an evolutionary algorithm and a randomised search algorithm for the dynamic vertex cover problem based on its dual formulation. The dynamic vertex cover problem has already…
We consider a mixed formulation of parametrized elasticity problems in terms of stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce conservation of linear and angular momentum. Due to the…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…