Related papers: Fast projection onto the top-k-sum constraint
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…
In the Euclidean $k$-center problem in sliding window model, input points are given in a data stream and the goal is to find the $k$ smallest congruent balls whose union covers the $N$ most recent points of the stream. In this model, input…
In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…
We are interested in the problem of finding $k$ nearest neighbours in the plane and in the presence of polygonal obstacles ($\textit{OkNN}$). Widely used algorithms for OkNN are based on incremental visibility graphs, which means they…
Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$…
Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple…
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
We address general-shaped clustering problems under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration. The algorithm has low computational complexity…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much less explored in the first-order optimization literature.…
In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set…
$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…
Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers,…
A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…
Utility-based shortfall risk (UBSR), a convex risk measure sensitive to tail losses, has gained popularity in recent years. However, research on computational methods for UBSR optimization remains relatively scarce. In this paper, we…
We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
We study efficient algorithms for the Euclidean $k$-Center problem, focusing on the regime of large $k$. We take the approach of data reduction by considering $\alpha$-coreset, which is a small subset $S$ of the dataset $P$ such that any…