摘要:

Tbe notion of quasi-interiorly e-tangent cones to multifunctions is considered. General properties as the sum of multifunctions, the composition of amultifunction with a mapping,... and the relationships with the e-tangent cones are studied.

ISSN:0163-0563    

DOI:10.1080/01630568908816323

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

In the present note we intröduce and investigate certain sequences of discrete positive linear operators and Boolean sum modifications of them. The mappings considered are obtained by discretizing a class of transformed convolution-type operators using Gaussian quadrature of appropriate order. For our operators and their modifications we prove pointwise Jackson-type theorems involving the first and second order moduli of smoothness, thus providing new and elegant proofs of earlier results by Timan, Telyakowskii, Gopengauz and DeVore. Due to their discrete structure, optimal order of approximation and ease of computation, the operators appear to be useful for numerical approximation. In an intermediate step we solve an old problem in Approximation Theory; its importance was only recently emphasized in a paper of Butzer.

ISSN:0163-0563    

DOI:10.1080/01630568908816324

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

We consider the problem for convex interpolation with minimal Lpnorm of the second derivative, 1 < p < +α. Convergence of a class of dual methods is established and numerical results are presented. It is proved that if p 2 then the solution of the problem is locally Lipschitz with respect to the data in the uniform metric.

ISSN:0163-0563    

DOI:10.1080/01630568908816325

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

An optimal shape design problem of an elastic body described by a system of two nonlinear elliptic equations is considered. The problem is to find the boundary of the domain occupied by the body in such a way that the stiffnes of the system in the equilibrium state is minimized.

ISSN:0163-0563    

DOI:10.1080/01630568908816326

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

The paper concerns solving a certain class of i11-posed problems including integral equationsof the first kind. The proposed regularization consists in replacing the considered i11-posedproblem by an ass ociated dynamical system. Well posedness of introduced system and an asymptotic connection of its solution with the solution we look for are proved.

ISSN:0163-0563    

DOI:10.1080/01630568908816327

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Convergence results for simplicia1 fixed point algorithms applied to problems in Banach-spaces enable constructive proofs of the existence of fixed points for set valued operators [14]. Boundary value problems for differential inclusions will be interpreted in this context. The resulting new algorithm allows numerical treatment of boundary value problems with Peano-typedynamics. The necessary conditions of the Pontryagin Maximum Principle are discussed in this framework, leading to a new indirect method for the computation of optimal trajectories with its focus on global convergence conditions for compact control domains.

ISSN:0163-0563    

DOI:10.1080/01630568908816328

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

An algorithm for solving the open-loop optimal control problem proposed by Y. Sakawa and Y. Shindo is analysed. The algorithm is essentially based on the use of the Pontriagin maximum principle. The convergence properties of the algorithm are investigated. It is established here, under weaker assumptions, that i) the algorithm is well-defined, ii) the cost functional monotonically decreases, iii) a weak necessary optimality condition is asymptotically verified, if the sequence of computational control parameters is bounded from above and from below.

ISSN:0163-0563    

DOI:10.1080/01630568908816329

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Let us consider equations in the formwhereis an open subset of a normed space; for any fixedand H(λ,.) are mappings from the closure Đ of a neighborhood D of the origin in a Banach spaceXinto a Banach space Y with. Let λ be a characteristic value of the pair (T, L) such that T - L(λ.) is a Fredholm mapping with nullity p and index s,p>s≥0 and. We shall introduce new sufficient conditions on L and H for (A, 0) being a bifurcation point of the above equations in the degenerate case when the results obtained in [1], [4], [6], [7]and [8]etc. are not applicable.

ISSN:0163-0563    

DOI:10.1080/01630568908816330

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

A problem of minimizing a quadratic function over the unit ball of l2is considered,the motivation being a minimum norm problem for the heat equation controlled by the constrained initial condition. A constructive method for finding an ε-solution is developed and its convergence rate is estimated. The dependence of the solution, on the data is studied.

ISSN:0163-0563    

DOI:10.1080/01630568908816331

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Formulae for differentiation with respect to the parameter of an integral over the set given by an inclusion are proposed. The case with bounded and unbounded set is discussed. Such formulae can be used for differentiation of probability functions. An algorithm for solving chance constrainted optimization problems is considered.

ISSN:0163-0563    

DOI:10.1080/01630568908816332

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor