Related papers: Instance Optimal Geometric Algorithms
The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…
We address the problem of finding an optimal policy in a Markov decision process under a restricted policy class defined by the convex hull of a set of base policies. This problem is of great interest in applications in which a number of…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total…
An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
This paper considers time-average optimization, where a decision vector is chosen every time step within a (possibly non-convex) set, and the goal is to minimize a convex function of the time averages subject to convex constraints on these…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Existing 3D instance segmentation methods are predominated by the bottom-up design -- manually fine-tuned algorithm to group points into clusters followed by a refinement network. However, by relying on the quality of the clusters, these…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee…
In this paper, we propose an exact general algorithm for solving non-convex optimization problems, where the non-convexity arises due to the presence of an inverse S-shaped function. The proposed method involves iteratively approximating…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal…
This paper presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…