摘要:

This paper presents new generalizations of the Farkas lemma. Using these results, known infinite dimensional Farkas type results are integrated into one theory. An application is given to duality theory in homogeneous programming.

ISSN:0163-0563    

DOI:10.1080/01630568708816244

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

A family of higher-order iterative methods for inverting a linear bounded operator in a Banach space is presented. This family depending on two integer parameters can be considered as hyperpower methods of [1]. A convergence Theorem is proved and an optimal class with respect to the efficiency index is determined . Several error bounds are derived and compared with those in the literature.

ISSN:0163-0563    

DOI:10.1080/01630568708816245

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

First order necessary optimality conditions for a minimum of an inequality constrained minimization problem are given in terms of approximate quasidifferentials, without the usual differentiability, convexity or locally Lipschitz assumptions. The main result is obtained with the help of a semi-infinite Gordan type alternative theorem. Sufficient conditions for a minimum are also given with the usual convexity assumption replaced by an invex condition.

ISSN:0163-0563    

DOI:10.1080/01630568708816246

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Using our theorems (of [12]) on separation of convex sets by linear operators, in the sense of the lexi-cographical order on Rn, we prove some theorems of surrogate duality for vector optimization problems with convex constraints (but no regularity assumption), where the surrogate constraint sets are generalized half-spaces and the surrogate multipliers are linear operators, or isomorphisms, or isometries. In the cae of inequality constraints, we prove that the surrogate multipliers can be taken lexicographically non-negative isometries or non-negative (in the usual order) linear isomorphisms.

ISSN:0163-0563    

DOI:10.1080/01630568708816247

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Based on Stummel's discrete approximation theory of normed spaces, a unified approach to the discrete approximation of set-valued and point-valued functions is introduced.

ISSN:0163-0563    

DOI:10.1080/01630568708816248

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

We consider a differential inclusion together with a sequence of general multistep methods. For the solutions of the approximate problems by discretization-theoretic tools we prove, under general assumptions, a convergence result ensuring the existence of a solution of the diffe rential inclusion simultaneously. This result is applied to set-valued analogues of linear m ultistep methods and Runge-Kutta methods as specifications of the general muitistep method.

ISSN:0163-0563    

DOI:10.1080/01630568708816249

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568708816250

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

By means of a general concept of consistent approximation a class of decomposition methods for solving nonlinear operator equations is described in order to treat known as well as new concrete algorithms. A rigorous local convergence analysis is given, and the methods belonging to the class are shown to be superlinearly convergent.

ISSN:0163-0563    

DOI:10.1080/01630568708816251

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

This note improves some results proved in [1,8] concerned with existence of cone-maximal points. We deal with a class of convex cones which is the largest possible to ensure the existence of maximal points in every weakly compact set. We show that every convex weakly compact set possesses maximal points which are extreme as well.

ISSN:0163-0563    

DOI:10.1080/01630568708816252

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

A fully discrete scheme for a class of multidimensional degenerate parabolic equations is proposed. The discretization is given by $supoesup piecewise linear finite elements in space and backward differences in time (the smoothing procedure is avoided). Numerical integration is used; hence the proposed method is easy to implement. Optimal error estimates in energy norms are proved for the solutions.

ISSN:0163-0563    

DOI:10.1080/01630568708816253

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor