Related papers: Approximate Dynamic Programming with Feasibility G…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a dynamic programming formulation that is…
Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online…
Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue.…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…
We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…
In the aftermath of an extreme natural hazard, community residents must have access to functioning food retailers to maintain food security. Food security is dependent on supporting critical infrastructure systems, including electricity,…
In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Our goal is to design distributed coordination strategies that enable agents to achieve global performance guarantees while minimizing the energy cost of their actions with an emphasis on feasibility for real-time implementation. As a…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
The multistage robust unit commitment (UC) is of paramount importance for achieving reliable operations considering the uncertainty of renewable realizations. The typical affine decision rule method and the robust feasible region method may…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…