Related papers: An Exact Algorithm for the Stratification Problem …
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear…
In this paper, we introduce a novel star partitioning problem for simple connected graphs $G=(V,E)$. The goal is to find a partition of the edges into stars that minimizes the maximum number of stars a node is contained in while…
We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on a stratified set and present a first-order algorithm designed to find a stationary point of that problem. Our assumptions on the…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marin proposed a…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
The apportionment problem deals with the fair distribution of a discrete set of $k$ indivisible resources (such as legislative seats) to $n$ entities (such as parties or geographic subdivisions). Highest averages methods are a frequently…
In the highway problem, we are given an n-edge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…
It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…