摘要:

Starting with the fact that the optimum in any linear programming problem over a certain. bounded region ist attained in at least one feasible basic solution, and that the number of feasible basic solutions is finite, the general linear programming problem is considered as a combinatorial programming problem. In order to solve this problem the extension principle die to Schoch is applied. According to the setSof feasible basic solutions of the original problem, a setRis defined which containsS. By successive reduction of the objective function, a sequence of subsetsUνRis formed. Moreover, a properly monotone increasing sequence {bν} of lower bounds for the value of the objective function is given. By making use of a discrepancy function, the author investigats, whetherUν andShave a non-empty intersection. the fitst non-empty intersectionUν ∩Swhich can be found represents the set of all optimal basic solutions of the initial problem.

ISSN:0047-6277    

DOI:10.1080/02331887508801197

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

This paper explains a new method for solving linear programming problems of largedimension, based on decomposition in columms of the starting problem. An exactly solving procedure is reclived by using primal simple algorithms. Furthermore, some statements about the computional realisation are given and their application to some special structure of the restriction matrix will be inquired. For the speical case of nonnegativ coefficient-matrix will be given an estimation for the optimal solution.

ISSN:0047-6277    

DOI:10.1080/02331887508801198

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

This paper deals with the Gomory all-integer algorithm and its modification to obtain integer solutions to linear fractional functionals programming (L.F.F.P.). First, we sholve a non integer L.F.F.P.-problem, then we define linear substitutional objective functions and derive important properties of them. we find the integer solution to the L.F.F.P.-problem by solving linear programming problems with these substitutinal objective functions. All cases, in which the integer L.F.F.P.-problem has a solution, are described and th4 algorithms, to find the optimal integer solution, are given. We can see, that there are more cases, in which the integer L.F.F.P.-problem has a solution than in finding a solution of the L.F.F.P.-problem due to Martos.

ISSN:0047-6277    

DOI:10.1080/02331887508801199

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

The mathematical and algorithmical aspects of the network model, which are the basis of the “Computer Programme System Network Technique” developed in the College of Civil Engineering Leipzig, are discussed in this paper. The general coupling conditions for proedures which are used lead to the common data calculation appearing as an essentially more general linear optimization problem than it is in the case in usual network models. Algorithms for calculating the lastest starting times are given as well as an algorithm for finding an admissible data-timesystem. The latter works by using a combinatorial optimization method similar to Minty's algorithm. A more detailed description of this method is presented.

ISSN:0047-6277    

DOI:10.1080/02331887508801200

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Based on an idea by Griffth and Stewart a general algorithm is presented for nonlinear programming problem with differentiable abjective function and restrivtions whose gradients satisfy the Lipschitz-condition and its convergence is probed.

ISSN:0047-6277    

DOI:10.1080/02331887508801201

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

The paper is based on the iterative procedure for the solution of extremal problems with constraints, whcih is due to Polyak. The advantages of the procedure are its generality, its suppositions being not very strict, its favourable properties from the point of view of calculation technique. However, if one studies the applicability of the procedure to the numerical difficulties may arise. The present paper deals with the mathematical difficulties. In particular an extension of the procedure with respect to a feasible direction is geiven. This is followed by ther investigation of the convergence of the extended procedure being considered here. In a further section the ascertainment of rupture criteria for some classes of nonlinear extremal problems is studied.

ISSN:0047-6277    

DOI:10.1080/02331887508801202

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

This paper presents a functional analytic model for a class of problems of optimal control, derives necessary optimality criterions and applies them to a feneralized version of Butkovski's problem and a modified version of Egorov' problem, in order to generalize and jistify their maximum principles.

ISSN:0047-6277    

DOI:10.1080/02331887508801203

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Norm foumlas are derived for Leontlef matrices to estimate errors resulting from input informations. They furnish different bounds in accordance with the underlying block structure.

ISSN:0047-6277    

DOI:10.1080/02331887508801204

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

The present paper deals with the stability analysis of economic systems. First of all a stability conception for economic systems id developed. The system under consideration is described as a dynamic, controlled and disturbed system. Nocessary and sufficient conditions for stability are given. The methods are demonstrated taking as example a dynamic multi-sector model and asuming investment controller.

ISSN:0047-6277    

DOI:10.1080/02331887508801205

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

M.L.Puri, P.K.Sen Nonparametric Methods in Multivariate Analysis John Wiley & Sons, New York 1971, XI, 440 S., £ 9.50.

ISSN:0047-6277    

DOI:10.1080/02331887508801206

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor