Related papers: Time discretization and quantization methods for o…
In this paper, we study unconstrained distributed optimization strongly convex problems, in which the exchange of information in the network is captured by a directed graph topology over digital channels that have limited capacity (and…
We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two…
Control strategies for dissipative preparation of target quantum states, both pure and mixed, and subspaces are obtained by switching between a set of available semigroup generators. We show that the class of problems of interest can be…
Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for…
We establish upper bounds for the $L^p$-quantization error, p in (1, 2+d), induced by the recursive Markovian quantization of a d-dimensional diffusion discretized via the Euler scheme. We introduce a hybrid recursive quantization scheme,…
We show that the optimal decision policy for several types of Bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions. This is established by using lattice programming and…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension, and also the analogous problem for a symmetric variant of the system. Assuming smoothness of solutions, we discretize these problems…
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
We propose a new numerical method for the computation of the optimal value function of perturbed control systems and associated globally stabilizing optimal feedback controllers. The method is based on a set oriented discretization of state…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…
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…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
Multi-stage stochastic optimization lies at the core of decision-making under uncertainty. As the analytical solution is available only in exceptional cases, dynamic optimization aims to efficiently find approximations but often neglects…
Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al.\ (\textit{Stat.\ Comput.}, 2017) proposed randomisation of…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…