Related papers: An efficient second-order cone programming approac…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
Large-scale machine learning models are often trained by parallel stochastic gradient descent algorithms. However, the communication cost of gradient aggregation and model synchronization between the master and worker nodes becomes the…
We propose an inexact decentralized dual gradient tracking method (iDDGT) for decentralized optimization problems with a globally coupled equality constraint. Unlike existing algorithms that rely on either the exact dual gradient or an…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…
Security-constrained unit commitment with alternating current optimal power flow (SCUC-ACOPF) is a central problem in power grid operations that optimizes commitment and dispatch of generators under a physically accurate power transmission…
Solving the Alternating Current Optimal Power Flow (AC OPF) problem to global optimality remains challenging due to its nonconvex quadratic constraints. In this paper, we present a unified framework that combines static piecewise…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
We present an algorithm that efficiently computes nearly-optimal solutions to a class of combinatorial reconfiguration problems on weighted, undirected graphs. Inspired by societally relevant applications in networked infrastructure…
This paper examines the performance trade-offs between an introduced linear flexibility market model for congestion management and a benchmark second-order cone programming (SOCP) formulation. The linear market model incorporates voltage…
Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers,…
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…
In this paper, we propose two novel Robin-type domain decomposition methods based on the two-grid techniques for the coupled Stokes-Darcy system. Our schemes firstly adopt the existing Robin-type domain decomposition algorithm to obtain the…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…
Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the…
In this work, we study the stochastic optimal control problem (SOC) mainly from the probabilistic view point, i.e. via the Stochastic Maximum principle (SMP) \cite{Peng4}. We adopt the sample-wise backpropagation scheme proposed in…