摘要:

In order to define the notion “solution” of an arbitary parametric linear programming problem with constant matrix of constraints whose coefficients of the objective function as well as the components of the right hand side vector depend in a very general manner on the parameters there are introduced some usefull notions. The most important among them is the “structure of a solution” which yields a partion of the setPof all parameters under consideration firstly into the unsolvability setP0and the solvability setPLwhich as complement toP0is an open set with respect toP. The setPLcan be divided into a finite number of maximal closed with respect toPsubsets which are characterized by a certain structure. The desired notion “solution” for a general parametric linear programming problem then represents finitely many pairs containing a partition set together with the corresponding structure. Besides of this mainly investigations there are studied unicity of a partition and related questions.

ISSN:0047-6277    

DOI:10.1080/02331887208801097

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor

摘要:

One possible way of solving a constrained optimization problem consists in its transformation into a sequence of unconstrained problems. In this paper is presented the connection between three of this methods; namely the method of centers (Huard), the SUMT (sequential unconstrained minimization technique) without parameters (Fiacco and Mccormick) and the method of barycenters (Lommatzsch). For the metyhod of centers is presented a simple proof of convergence without convexity assumptions, developed from an idea of Huard Further are given relations between some regularity conditions, which were used for this methods.

ISSN:0047-6277    

DOI:10.1080/02331887208801098

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor

摘要:

The present paper is concerned with the problem of approximating a given element of a linear space by a family of elements, depending on a parameter, as well as possible. Normlike convex functionals are used as measures for the quality of approximation. By means of quasilinearization of the convex approximation measure the approximation problem is transformed into a maximin. or programming problem, which is sometimes dealt with much easier. From the maximim-formulation a dual problem, replacing the primal approximation problems, is derived with the aid of a maximin-theorem of Ky Fan. New resultats on linear Chebyshev approximation with restricted parameters are obtained in this manner.

ISSN:0047-6277    

DOI:10.1080/02331887208801099

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor

摘要:

The service model of Erlang withnservers, Poisson input, and exponential distributed service times isgeneralized in such a way that one can consider service times which can be dependent and have arbitary distributions. A sufficient condition is given for the existence of a uniquely determined stationary distribution for the state of the system. As in the case of the usual Erlang model, this distribution can be described by the well known Erlang formulas. The condition requires that the service times of different servers form stationary series which are independent of each other.

ISSN:0047-6277    

DOI:10.1080/02331887208801100

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor

摘要:

Because the necessary conditions for optimal stratifications, the socalled Dalenius-equations, sometimes, have more than one solution, it is shown, how in the case of a small number of strata it is possible to find the whole set of solution using an iterative analog computer. With the aid of the sufficient conditions it can be checked, whether a solution leads to a relative minimum or not.

ISSN:0047-6277    

DOI:10.1080/02331887208801101

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor

摘要:

If the errors of a linear model are normally distributed and if quadratic loss is used, it is known, that the Gauss-Markov-estimatoris the best unbiased estimator of an estimable function η. Under certain conditions this is also true for convex loss. It we know only, that the error distribution lies in a certain class of distributions, and the normal distribution is in this class too, then, it is shown, thatbecomes minimax relative to this class.

ISSN:0047-6277    

DOI:10.1080/02331887208801102

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor

摘要:

M.Bliefernich, M.Grych, M.Pfeifer, C.J.Wagner: Aufgaben zur Matrizenrechnung und linearen Optimierung — mit ausführlichen Lösungen — 3. Auflage (berichtigter Nachdruck der zweiten Auflage Verlag Die Wirtschaft, Berlin 1971 310 S., 14,50 M.

ISSN:0047-6277    

DOI:10.1080/02331887208801103

出版商:Akademie-Verlag    

年代:1972

数据来源: Taylor