Related papers: Adversarial Obstacle Placement with Spatial Point …
Suppose we are given a pair of points $s, t$ and a set $S$ of $n$ geometric objects in the plane, called obstacles. We show that in polynomial time one can construct an auxiliary (multi-)graph $G$ with vertex set $S$ and every edge labeled…
We investigate the distributed DC-Optimal Power Flow (DC-OPF) problem for a dynamic and uncertain environment. The unpredictable supply of renewable resources and varying prices of the electricity market are a few factors responsible for…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
Uncertainties arising from localization error, trajectory prediction errors of the moving obstacles and environmental disturbances pose significant challenges to robot's safe navigation. Existing uncertainty-aware planners often approximate…
Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…
The packet routing problem asks to select routing paths that minimize the maximum edge congestion for a set of packets specified by source-destination vertex pairs. We revisit a semi-oblivious approach to this problem: each…
Planning safe paths is a major building block in robot autonomy. It has been an active field of research for several decades, with a plethora of planning methods. Planners can be generally categorised as either trajectory optimisers or…
This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time…
Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…
The Thief Orienteering Problem (ThOP) is a multi-component problem that combines features of two classic combinatorial optimization problems: Orienteering Problem and Knapsack Problem. The ThOP is challenging due to the given time…
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.…
The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing…
The input to the stochastic orienteering problem consists of a budget $B$ and metric $(V,d)$ where each vertex $v$ has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are…
Recently, convex nested stochastic composite optimization (NSCO) has received considerable attention for its applications in reinforcement learning and risk-averse optimization. The current NSCO algorithms have worse stochastic oracle…
This paper optimizes the configuration of large-scale data centers toward cost-effective, reliable and sustainable cloud supply chains. The problem involves placing incoming racks of servers within a data center to maximize demand coverage…
In image classification tasks, the evaluation of models' robustness to increased dataset shifts with a probabilistic framework is very well studied. However, object detection (OD) tasks pose other challenges for uncertainty estimation and…
Collision-free mobile robot navigation is an important problem for many robotics applications, especially in cluttered environments. In such environments, obstacles can be static or dynamic. Dynamic obstacles can additionally be…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…