摘要:

LetAbe an operator from a real Banach space into a real Hilbert space. In this paper we study least squares regularization methods for the ill-posed operator equationA(u) =fusing nonlinear nondifferentiable penalty functionals. We introduce a notion of distributional approximation, and use constructs of distributional approximations to establish convergence and stability of approximations of bounded variation solutions of the operator equation. We also show that the results provide a framework for a rigorous analysis of numerical methods based on Euler-Lagrange equations to solve the minimization problem. This justifies many of the numerical implementation schemes of bounded variation minimization that have been recently proposed.

ISSN:0163-0563    

DOI:10.1080/01630569808816863

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Recently Deutsch, Li and Swetits [2] have studied, in Hilbert space, a dual problem (Qm) to the primal problem (P) of minimization of a special class of convex functionsfover the intersection ofmclosed convex sets, wheremis finite. In the first part of this paper we obtain, in a locally convex space, some results on problem (Qm) and on its relations with the usual Lagrangian dual problem (Q) to (P) (studied in [9]), in the case when (P) has a solution. In the second part we give some applications to duality for the distance to the intersection ofmclosed convex sets in a normed linear space, in the case when a nearest point exists. Most of our results seem to be new even in the particular cases studied in [9] (the casem= 1), [l] (duality formulas for the distance to the intersection ofmclosed half-spaces in a normed linear space) and [2].

ISSN:0163-0563    

DOI:10.1080/01630569808816864

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Two systems of variational equations and inequalities, which characterize the solution of a distributed elliptic control problem governed by the Laplacian with pointwise control and state constraints respectively, are discretized by a mixed finite element method using piecewise linear shape functions. The resulting error estimates of the approximation of the optimal state are derived inH1,2,whereas the corresponding error estimates for the optimal control are given inL2, if the cost functional is strictly coercive, otherwise in negative norms.

ISSN:0163-0563    

DOI:10.1080/01630569808816865

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569808816837

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor