摘要:

Using generalized inverse matrices we construct cuts often being deeper than all cuts of the GOMORY group. The reason for this is that not only the aotive conditions in the continuous optimum are mentioned, but in a sense global considerations are made.

ISSN:0047-6277    

DOI:10.1080/02331887508801262

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

The GOMORY algorithm is used to obtain the mixed-integer solution to linear fractional functionals programming (L.F.F.P.). All cases, in which the mixed-integer L.F.F.P.-problem has a solution, are described and algorithms to find the optimal mixed-integer solution are given.

ISSN:0047-6277    

DOI:10.1080/02331887508801263

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Being based on the theoretical considerations presented in part I a general solution procedure is given, which during the process uses basic solutions with negative components, too. Criteria for the variables which have to enter the basis solution and for those which have to leave it are proposed. Hereby the value of the discrepancy does not increase. The first basis solutionwithis discussed. The case, in which the objective function is unbounded over the feasible region is considered in details. Then by specification the primal-dual algorithm and a primal simplex method are developed from the general solution procedure.

ISSN:0047-6277    

DOI:10.1080/02331887508801264

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

We show in this note that certain minimality and complementarity properties of the s.c. Z-functions, which were introduced and discussed by A. TAMIR, follow directly from a theorem due to GEORG WINTGEN, published in 1964.

ISSN:0047-6277    

DOI:10.1080/02331887508801265

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

For GORDAN's alternative theorem on linear inequalities, which appeared 100 years ago, besides of some historical remarks and geometrical explanations a new proof is presented, It is shown, that GORDAN's theorem also can serve as a key theorem for the theory of linear inequalities.

ISSN:0047-6277    

DOI:10.1080/02331887508801266

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In the present paper strict linear inequalities in theRnwit respect ot polyhedral semi-orderings are studied. A general alternative theorem reminding to a corresponding GORDAN theorem and a general existence theorem being similar to the TUCKER theorem are stated. In order to treat strict inequalities the conception of partially open polyhedral cones and a calculus for its strict dualization are developed. The corresponding strict semi-orderings are formed, too.

ISSN:0047-6277    

DOI:10.1080/02331887508801267

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In this work pairs of dual linear programming problems in reflexive BANACH spaces with linear continuous operators in the constraints are treated. Sufficient conditions for the existence of optimal solutions and the duality relation are given. These general conditions are used for the investigation of linear problems inLp-spaces with weak singular FREDHOLM integral operators. Another example deals with problems in the product spaceLp×Rm.

ISSN:0047-6277    

DOI:10.1080/02331887508801268

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In order to extend the duality theory for convex extremal problems to topological linear spaces, the conception of stable functions introduced by STORE is extended to general spaces and arbitrary functions. A related to STOER's duality theorem is proved from which follows e.g. FENCHEL's theorem in different topologies. Finally, the relations to other duality theories and some necessary and sufficient optirnality conditions are surveyed.

ISSN:0047-6277    

DOI:10.1080/02331887508801269

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In this note a generalization of a result of ZOWE on FENCHEL's duality theorem is given, where, in addition, the assumptions are weakened.

ISSN:0047-6277    

DOI:10.1080/02331887508801270

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

A theorem about the structure of optimal solutions of linear programming problems with a finite number of scalar restrictions and with upper bounded variables in order complete topological vector lattices is proved. This theorem is a generalization of the well-known NEYMAN-PEARSON-Lemma.

ISSN:0047-6277    

DOI:10.1080/02331887508801271

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor