相关论文: Chasing Nested Convex Bodies Nearly Optimally

Convex Optimization with Nested Evolving Feasible Sets (CONES)} is considered where the objective function $f$ remains fixed but the feasible region evolves over time as a nested sequence $S_1 \supseteq S_2 \supseteq \cdots \supseteq S_T$.…

Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving…

We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…

We develop polynomial-time algorithms for near-optimal minimax mean estimation under $\ell_2$-squared loss in a Gaussian sequence model under convex constraints. The parameter space is an origin-symmetric, type-2 convex body $K \subset…

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 Weber problem consists of finding a point in $\mathbbm{R}^n$ that minimizes the weighted sum of distances from $m$ points in $\mathbbm{R}^n$ that are not collinear. An application that motivated this problem is the optimal location of…

This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…

Fitting parametric models of human bodies, hands or faces to sparse input signals in an accurate, robust, and fast manner has the promise of significantly improving immersion in AR and VR scenarios. A common first step in systems that…

Let $(X, d)$ be a metric space and $C \subseteq 2^X$ -- a collection of special objects. In the $(X,d,C)$-chasing problem, an online player receives a sequence of online requests $\{B_t\}_{t=1}^T \subseteq C$ and responds with a trajectory…

Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…

We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is…

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…

We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…

We present algorithms for the $(1+\epsilon)$-approximate version of the closest vector problem for certain norms. The currently fastest algorithm (Dadush and Kun 2016) for general norms has running time of $2^{O(n)} (1/\epsilon)^n$. We…

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…

In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…