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We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the…
This article focuses on a nonlinear Neumann boundary feedback control formulation for the viscous Burgers' equation and develops a class of finite difference schemes to achieve global stabilization. The proposed procedure, known as the…
Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is a hard task in numerical analysis. Solving a design…
We analyze a high order unfitted hybridizable discontinuous Galerkin (HDG) method for an optimal control problem governed by a convection-diffusion equation posed in a domain with piecewise-wise $\mathcal{C}^2$ boundary $\partial \Omega$.…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
The paper presents a distributed model predictive control (DMPC) scheme for continuous-time nonlinear systems based on the alternating direction method of multipliers (ADMM). A stopping criterion in the ADMM algorithm limits the iterations…
This paper presents a distributed model predictive control (DMPC) scheme for nonlinear continuous-time systems. The underlying distributed optimal control problem is cooperatively solved in parallel via a sensitivity-based algorithm. The…
Chance constrained programming (CCP) is a powerful framework for addressing optimization problems under uncertainty. In this paper, we introduce a novel Gradient-Guided Diffusion-based Optimization framework, termed GGDOpt, which tackles…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
Finite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique solution to optimal control problems is guaranteed based on…
This paper is concerned with the designing, analyzing and implementing linear and nonlinear discretization scheme for the distributed optimal control problem (OCP) with the Cahn-Hilliard (CH) equation as constrained. We propose three…
Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
We consider differentiability issues associated to the problem of minimizing the accumulation of a granular cohesionless material on a certain surface. The design variable or control is determined by source locations and intensity thereof.…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…