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We present a procedure to numerically compute finite step worst case performance guarantees on a given algorithm for the unconstrained optimization of strongly convex functions with Lipschitz continuous gradients. The solution method provided serves as an alternative approach to that derived by Taylor, Hendrickx, and Glineur in [Math. Prog. 161 (1-2), 2017]. The difference lies in the fact that our solution uses conditions for the interpolation of a set of points and gradient evaluations by the gradient of a function in the class of interest, whereas their solution uses conditions for the interpolation of a set of points, gradient evaluations, and function evaluations by a function in the class of interest. The motivation for this alternative solution is that, in many cases, neither the algorithm nor the performance metric of interest rely upon function evaluations. The primary development is a procedure to avoid suffering from the factorial growth in the number of these conditions with the size of the set to be interpolated when solving for the worst case performance.
Traffic Management in Advanced Aerial Mobility (AAM) inherits many elements of conventional Air Traffic Management (ATM), but brings new complexities and challenges of its own. One of its ways of guaranteeing separation is the use of airborne, stand-
In this paper, we propose a notion of high-order (zeroing) barrier functions that generalizes the concept of zeroing barrier functions and guarantees set forward invariance by checking their higher order derivatives. The proposed formulation guarante
New forms of on-demand transportation such as ride-hailing and connected autonomous vehicles are proliferating, yet are a challenging use case for electric vehicles (EV). This paper explores the feasibility of using deep reinforcement learning (DRL)
Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist numerous applic
In this paper, we propose a new automaton property of N-step nonblockingness for a given positive integer N. This property quantifies the standard nonblocking property by capturing the practical requirement that all tasks be completed within a bounde