相关论文: Duality-based a posteriori error estimates for som…

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the…

In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…

The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity…

We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to…

In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are studied for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and…

This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…

We analyze a reliable and efficient max-norm a posteriori error estimator for a control-constrained, linear-quadratic optimal control problem. The estimator yields optimal experimental rates of convergence within an adaptive loop.

It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a…

The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncertain) parameters. We introduce a two-level a posteriori…

We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the…

This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…

This paper studies parameterized stochastic optimization problems in finite discrete time that arise in many applications in operations research and mathematical finance. We prove the existence of solutions and the absence of a duality gap…

We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in…

In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case…

We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order discontinuous Galerkin temporal discretizations.…

We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…