相关论文: A Moment and Sum-of-Squares Extension of Dual Dyna…

Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…

Parameterized Sequential Decision Making (Para-SDM) framework models a wide array of network design applications spanning supply-chain, transportation, and sensor networks. These problems entail sequential multi-stage optimization…

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…

Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based on deep neural networks (DNNs) often lack convergence…

The increasing penetration of renewable energy requires greater use of storage resources to manage system intermittency. As a result, there is growing interest in evaluating the opportunity cost of stored energy, or usage values, which can…

This paper presents algorithms that upper-bound the peak value of a state function along trajectories of a continuous-time system with rational dynamics. The finite-dimensional but nonconvex peak estimation problem is cast as a convex…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO). We generalize the usual consecutive dual dynamic programming (DDP) algorithm to DR-MCO and propose…

In this brief, we present an enhanced privacy-preserving distributed estimation algorithm, referred to as the ``Double-Private Algorithm," which combines the principles of both differential privacy (DP) and cryptography. The proposed…

This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…

This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves a discretely divergence-free (DDF) constraint on the…

We consider a finite-state partially observable Markov decision problem (POMDP) with an infinite horizon and a discounted cost, and we propose a new method for computing a cost function approximation that is based on features and…

We consider a general aggregation framework for discounted finite-state infinite horizon dynamic programming (DP) problems. It defines an aggregate problem whose optimal cost function can be obtained off-line by exact DP and then used as a…

We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However, many DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space…

The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space,…

This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…

We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…