Related papers: Greedy algorithms for high-dimensional non-symmetr…
The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…
We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of lines in a very short time and also produces…
Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation, which involves adaptively selecting…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
This work studies a class of non-smooth decentralized multi-agent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common non-smooth term. We propose a general primal-dual…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
We analyse the problem of controllability for parameter-dependent linear finite-dimensional systems. The goal is to identify the most distinguished realisations of those parameters so to better describe or approximate the whole range of…
We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
We study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…
In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…
The nonlinear Kaczmarz method was recently proposed to solve the system of nonlinear equations. In this paper, we first discuss two greedy selection rules, i.e., the maximum residual and maximum distance rules, for the nonlinear Kaczmarz…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
We consider meshless approximation for solutions of boundary value problems (BVPs) of elliptic Partial Differential Equations (PDEs) via symmetric kernel collocation. We discuss the importance of the choice of the collocation points, in…
In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…