Related papers: Chasing Nested Convex Bodies Nearly Optimally
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Finding approximate stationary points, i.e., points where the gradient is approximately zero, of non-convex but smooth objective functions $f$ over unrestricted $d$-dimensional domains is one of the most fundamental problems in classical…
This paper introduces a novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations. By addressing…
We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\varepsilon)$-approximation algorithm for…
Lagrangian relaxation and approximate optimization algorithms have received much attention in the last two decades. Typically, the running time of these methods to obtain a $\epsilon$ approximate solution is proportional to…
In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To…
We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…
Chv\'{a}tal and Klincsek (1980) gave an $O(n^3)$-time algorithm for the problem of finding a maximum-cardinality convex subset of an arbitrary given set $P$ of $n$ points in the plane. This paper examines a generalization of the problem,…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be non-convex, while incurring a movement cost when changing actions between rounds. We ask: \textit{under what general…
We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on the leader's decision. The resulting random variable is…
We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show…
In this paper we consider the problem of constructing numerical algorithms for approximating of convex compact bodies in d-dimensional Euclidean space by polytopes with any given accuracy. It is well known that optimal with respect to the…
To facilitate effective, safe deployment in the real world, individual robots must reason about interactions with other agents, which often occur without explicit communication. Recent work has identified game theory, particularly the…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric…
In convex optimization, the problem of finding near-stationary points has not been adequately studied yet, unlike other optimality measures such as the function value. Even in the deterministic case, the optimal method (OGM-G, due to Kim…
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…
We show that any $n\times m$ matrix $A$ can be approximated in operator norm by a submatrix with a number of columns of order the stable rank of $A$. This improves on existing results by removing an extra logarithmic factor in the size of…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…