相关论文: Multilevel Picard scheme for solving high-dimensio…

Nonlinear model predictive control has been widely adopted to manipulate bilinear systems with dynamics that include products of the inputs and the states. These systems are ubiquitous in chemical processes, mechanical systems, and quantum…

We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…

We investigate the problem of coordinating multiple automated vehicles (AVs) in confined areas. This problem can be formulated as an optimal control problem (OCP) where the motion of the AVs is optimized such that collisions are avoided in…

The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the…

Leveraging the concept of the macroscopic fundamental diagram (MFD), perimeter control can alleviate network-level congestion by identifying critical intersections and regulating them effectively. Considering the time-varying nature of…

Multilevel programming is the standard framework for modeling hierarchical decision-making. In this paper, we characterize the computational complexity of deciding the existence of feasible and optimal solutions, as well as computing the…

Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…

The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…

Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…

Large-scale Markov decision processes (MDPs) require planning algorithms with runtime independent of the number of states of the MDP. We consider the planning problem in MDPs using linear value function approximation with only weak…

A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…

This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…

Current structural pruning methods face two significant limitations: (i) they often limit pruning to finer-grained levels like channels, making aggressive parameter reduction challenging, and (ii) they focus heavily on parameter and FLOP…

We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…

Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet…

Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important…

We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…