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The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper 10.1016/j.ejor.2014.05.042, the…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
Urban air mobility (UAM) has the potential to revolutionize our daily transportation, offering rapid and efficient deliveries of passengers and cargo between dedicated locations within and around the urban environment. Before the…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…
A linear programming (LP) model is proposed to improve the performance of a controlled freeway during an emergency evacuation. Based on reasonable assumptions, the main relationships among key factors are kept without the uncertain impact…
The inherent complexity of boundary plasma, characterized by multi-scale and multi-physics challenges, has historically restricted high-fidelity simulations to scientific research due to their intensive computational demands. Consequently,…
A novel deep multi-agent reinforcement learning framework is proposed to identify and resolve conflicts among a variable number of aircraft in a high-density, stochastic, and dynamic sector. Currently the sector capacity is constrained by…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. We establish that these problems are related to certain infinite-dimensional linear…
A conflict graph represents logical relations between binary variables, and effective use of the graph can significantly accelerate branch-and-cut solvers for mixed-integer programming (MIP). In this paper we develop efficient parallel…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
We address the multi-satellite scheduling problem with limited observation capacities that arises from the need to observe a set of targets on the Earth's surface using imaging resources installed on a set of satellites. We define and…
Autonomous motion planning is challenging in multi-obstacle environments due to nonconvex collision avoidance constraints. Directly applying numerical solvers to these nonconvex formulations fails to exploit the constraint structures,…
A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…
In this paper, the trajectory planning problem for autonomous rendezvous and docking between a controlled spacecraft and a tumbling target is addressed. The use of a variable planning horizon is proposed in order to construct an appropriate…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…
We present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory representation built upon…
A control optimization approach is presented for a chaser spacecraft tasked with maintaining proximity to a target space object while avoiding collisions. The target object trajectory is provided numerically to account for both passive…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…