Wenbin Liu

Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

In this paper, sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach. Our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work.

A Posteriori Error Estimates for Distributed Convex Optimal Control Problems

In this paper, we present an a posteriori error analysis for finite element approximation of distributed convex optimal control problems. We derive a posteriori error estimates for the coupled state and control approximations under some assumptions which hold in many applications. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for control problems. Explicit estimates are obtained for some model problems which frequently appear in real-life applications.

DEA models with undesirable inputs and outputs

Data Envelopment Analysis (DEA) models with undesirable inputs and outputs have been frequently discussed in DEA literature, e.g., via data transformation. These studies were scatted in the literature, and often confined to some particular applications. In this paper we present a systematic investigation on model building of DEA without transferring undesirable data. We first describe the disposability assumptions and a number of different performance measures in the presence of undesirable inputs and outputs, and then discuss different combinations of the disposability assumptions and the metrics. This approach leads to a unified presentation of several classes of DEA models with undesirable inputs and/or outputs.

A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs

This paper is primarily concerned with data envelopment analysis (DEA) of systems where negative outputs and negative inputs arise naturally. Examples of situations in which both negative inputs and negative outputs occur are given. More attention has been paid, in the literature, to the former type of problem. Most available DEA software does not solve this type of problem or copes with negative outputs and possibly negative inputs by assigning zero weights to them. A modified slacks-based measure (MSBM) model is presented, in which both negative outputs and negative inputs occur. The MSBM model overcomes the lack of translation invariance in the slacks-based measure model by drawing on the ideas from the range directional model (RDM). The MSBM model takes into account individual input and output slacks, which provides more precise evaluation of inefficient decision-making units (DMUs). It therefore, generally leads to lower efficiencies for inefficient DMUs than the RDM.

A posteriori error estimates for optimal control problems governed by parabolic equations

Summary. In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive finite element approximation schemes for the control problem.

Local A Posteriori Error Estimates for Convex Boundary Control Problems

In this paper, we derive some improved a posteriori error estimates for finite element approximation of Neumann boundary control problems. We first establish local upper a posteriori error estimates for both the state and the control approximation of the general convex boundary control problems. We then derive local upper and lower a posteriori error estimates for a class of control problems that frequently appear in applications.

A Posteriori Error Estimates for Control Problems Governed by Stokes Equations

In this paper, we derive a posteriori error estimates for the finite element approximation of distributed optimal control problems governed by the Stokes equations. We obtain a posteriori error estimators for both the state and the control approximation in the L2 norm and the H1 norm. These estimates can be used to construct reliable adaptive finite element approximation for the control problems.

Finite element approximation of the parabolic p -Laplacian

In this paper the authors consider the continuous piecewise linear finite element approximation in space of the following problem: Given

Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems

p \in (1,\infty )

A posteriori error estimates for discontinuous Galerkin time-stepping method for optimal control problems governed by parabolic equations

, f and