摘要:

Minimization problems in Hilbert space with quadratic objective function and closed convex constraint setCare considered. In case the minimum is not unique we are looking for the solution of minimal norm. If a problem is ill-posed, i.e. if the solution does not depend continuously on the data, and if the data are subject to errors then it has to be solved by means of regularization methods. The regularizing properties of some gradient projection methods—i.e. convergence for exact data, order of convergence under additional assumptions on the solution and stability for perturbed data—are the main issues of this paper.

ISSN:0163-0563    

DOI:10.1080/01630569208816489

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

In this paper, we apply the coupling of the boundary integral and finite element methods to study the weak solvability of certain nonmonotone nonlinear exterior boundary value problems. In order to convert the original exterior problem into an equivalent nonlocal boundary value problem on a finite region, we employ two different approaches based on the use of one and two integral equations on the coupling boundary. Existence of a solution for the associated weak formulation, and convergence properties of the corresponding Galerkin approximations are deduced from fundamental results in nonlinear functional analysis. Indeed, the main arguments of our proofs are based on a surjectivity theorem for mappings of type (S) and on the Fredholm alternative for nonlinear A-proper mappings.

ISSN:0163-0563    

DOI:10.1080/01630569208816490

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

In this paper, we discuss the parallel solution of variational inequalities on a general closed convex setK. First a sufficient and necessary condition will be given for the convergence of the parallel algorithm proposed in [10] which is suitable only in the case ofKbeing a closed convex cone. Second we present algorithms which work for the parallel computations on general closed convex sets. After that the parallel solution of linear complementary systems related to variational inequalities will be investigated. Finally numerical experiments will be reported to show the convergence of the algorithms.

ISSN:0163-0563    

DOI:10.1080/01630569208816491

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

In this paper a general theorem is proved about convergence and error estimates for Newton's method. It contains as special cases a theorem of Kantorowitsch-type, a theorem with nonlinear majorants and componentwise error estimates as well as a theorem of monotone type.

ISSN:0163-0563    

DOI:10.1080/01630569208816492

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

To anycorresponds a domainT(x) ⊂⊂Y= ]0, 1[2. For some ε > 0, the domain Ω is occupied by a quasiperiodic structure which has the property that if an ε-neighborhood ofxis enlarged by the scale factor (1/ε) then it appears like aY-periodically perforated piece of material, with holes “slightly different” fromT(x). The torsion problem of this structure is studied. The homogenization procedure is completed, that is all the convergences which reveal the system which governs the limit phenomenon, when ε → 0, are proved. In the periodic case there are already two distinct approaches to this problem: [1] and [2], The present work is based on them and on the stepwise method [3] used for proving the homogenization of linear elliptic equations with quasiperiodic coefficients.

ISSN:0163-0563    

DOI:10.1080/01630569208816493

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

A simple model optimal control problem for continuous casting with state-space constraints is approximated, as usual, by a penalty method and by a numerical discretization of the nonlinear heat equation. The convergence of the approximate problems directly to the original problem is proven under a stability criterion linking the penalty parameter with the discretization parameters. For this purpose, known discretization error estimates for the Stefan problem are extended for the case of time varying boundary conditions.

ISSN:0163-0563    

DOI:10.1080/01630569208816494

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Approximations of random operator equations are considered where the stochastic inputs and the underlying deterministic equation are approximated simultaneously. The main convergence result asserts that, under reasonable and verifiable assumptions, a sequence of weak solutions of approximate random equations converges weakly to a weak solution of the original equation. It is shown that this theorem extends and unifies results already known. We apply our theory to approximations of random differential equations involving stochastic processes with discontinuous paths and to projection methods for nonlinear random Hammerstein integral equations in spaces of integrable functions.

ISSN:0163-0563    

DOI:10.1080/01630569208816495

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

This paper shows how the Steiner selection has very nice properties in view of differentiability, measurability, and integrability of multi-functions.

ISSN:0163-0563    

DOI:10.1080/01630569208816496

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

It is the purpose of this paper to introduce iterative counterparts to the regularization method of Tikhonov-Phillips with general regularization (or smoothing) operators,To this effect, an explicit formula for the regularized approximationsxαis determined which has the formwherex0represents a certain well-posed component ofxT=KL−andrα(λ) = (λ + α)−1.L−is a generalized inverse ofLintroduced earlier by Eldén; it depends on the underlying operatorK. The iterative algorithms will be defined by replacing the rational functionsrαby adequate polynomials. The methods to be considered—including thepreconditioned conjugate gradient method—are highly efficient because they admit a recursive computation of the regularized approximations and because the generalized inverseL−need not be computed explicity. This is shown for a model problem whereLis a discretization of the derivative operator.

ISSN:0163-0563    

DOI:10.1080/01630569208816497

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Many inverse heat conduction problems lead us to consider the following noncharacteristic Cauchy problem for parabolic equations of the form“surface temperature”“surface heat flux”wherepis an elliptic operator, ϕ andgare given functions. This problem is well-known to be severely ill-posed, and up to now there have been many approaches for solving it in a stable way. However, most of them need a supplementary condition: either the initial condition, or a boundary condition, etc ⃜In this paper a variational method for this problem is suggested. In contrast to the other works, in the paper the initial condition is not assumed to be known. A short discussion on using the gradient methods is also given.

ISSN:0163-0563    

DOI:10.1080/01630569208816498

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor