Related papers: An Inexact Alternating Direction Method of Multipl…
The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex…
Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…
This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising explicit schemes are associated with explicit-implicit…
The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…
The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to…
Quantization of the parameters of machine learning models, such as deep neural networks, requires solving constrained optimization problems, where the constraint set is formed by the Cartesian product of many simple discrete sets. For such…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…
We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation…
The alternating direction method of multipliers (ADMM) is an effective method for solving wide fields of convex problems. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it is expensive…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…