Related papers: A Ray Intersection Algorithm for Fast Growth Dista…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
This paper presents a set of simple and intuitive robot collision detection algorithms that show substantial scaling improvements for high geometric complexity and large numbers of collision queries by leveraging hardware-accelerated ray…
The split covariance intersection filter (split CIF) is a useful tool for general data fusion and has the potential to be applied in a variety of engineering tasks. An indispensable optimization step (referred to as w-optimization) involved…
This paper studies the convergence properties the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple…
In the maximum independent set of convex polygons problem, we are given a set of $n$ convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…
We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…
Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center…
In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance…
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…
The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest…
Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…
The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature,…
This paper explores the distance-based relative state estimation problem in large-scale systems, which is hard to solve effectively due to its high-dimensionality and non-convexity. In this paper, we alleviate this inherent hardness to…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…