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  • 2005-2009
  • 1995-1999  (9)
  • 1997  (9)
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Material
Years
  • 2005-2009
  • 1995-1999  (9)
Year
Keywords
Language
  • 1
    Electronic Resource
    Electronic Resource
    Book reviews (1997)
    Springer
    Mathematical methods of operations research 46 (1997), S. 281-284 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217696
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
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    Cutting Plane Algorithms for Semidefinite Relaxations (1997)
    Details
    Publication Date: 2014-02-26
    Description: We investigate the potential and limits of interior point based cutting plane algorithms for semidefinite relaxations on basis of implementations for max-cut and quadratic 0-1 knapsack problems. Since the latter has not been described before we present the algorithm in detail and include numerical results.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 3
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    The Intersection of Knapsack Polyhedra and Extensions (1997)
    Details
    Publication Date: 2014-02-26
    Description: This paper introduces a scheme of deriving strong cutting planes for a general integer programming problem. The scheme is related to Chvatal-Gomory cutting planes and important special cases such as odd hole and clique inequalities for the stable set polyhedron or families of inequalities for the knapsack polyhedron. We analyze how relations between covering and incomparability numbers associated with the matrix can be used to bound coefficients in these inequalities. For the intersection of several knapsack polyhedra, incomparabilities between the column vectors of the associated matrix will be shown to transfer into inequalities of the associated polyhedron. Our scheme has been incorporated into the mixed integer programming code SIP. About experimental results will be reported.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 4
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    Set Packing Relaxations of Some Integer Programs (1997)
    Details
    Publication Date: 2020-08-05
    Description: This paper is about {\em set packing relaxations\/} of combinatorial optimization problems associated with acyclic digraphs and linear orderings, cuts and multicuts, and vertex packings themselves. Families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 5
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    The Steiner tree packing problem in VLSI design (1997)
    Details
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 6
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    Test sets of the knapsack problem and simultaneous diophantine approximation (1997)
    Details
    Publication Date: 2014-02-26
    Description: This paper deals with the study of test sets of the knapsack problem and simultaneous diophantine approximation. The Graver test set of the knapsack problem can be derived from minimal integral solutions of linear diophantine equations. We present best possible inequalities that must be satisfied by all minimal integral solutions of a linear diophantine equation and prove that for the corresponding cone the integer analogue of Caratheodory's theorem applies when the numbers are divisible. We show that the elements of the minimal Hilbert basis of the dual cone of all minimal integral solutions of a linear diophantine equation yield best approximations of a rational vector ``from above''. A recursive algorithm for computing this Hilbert basis is discussed. We also outline an algorithm for determining a Hilbert basis of a family of cones associated with the knapsack problem.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 7
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    Hilbert bases of cones related to simultaneous Diophantine approximations and linear Diophantine equations (1997)
    Details
    Publication Date: 2014-02-26
    Description: This paper investigates properties of the minimal integral solutions of a linear diophantine equation. We present best possible inequalities that must be satisfied by these elements which improves on former results. We also show that the elements of the minimal Hilbert basis of the dual cone of all minimal integral solutions of a linear diophantine equation yield best approximations of a rational vector ``from above''. Relations between these cones are applied to the knapsack problem.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 8
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    Contributions to General Mixed Integer Knapsack Problems (1997)
    Details
    Publication Date: 2014-02-26
    Description: This paper deals with a general mixed integer knapsack polyhedron for which we introduce and analyze a new family of inequalities. We discuss the value of this family both from a theoretic and a computational point of view.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 9
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    Discrete Relaxations of Combinatorial Programs (1997)
    Details
    Publication Date: 2020-08-05
    Description: This paper investigates {\em relations\/} among combinatorial optimization problems. To establish such relations we introduce a transformation technique \mbox{---{\em aggregation}---} that allows to relax an integer program by means of another integer program. We prove that various families of prominent inequalities for the acyclic subdigraph problem, the multiple knapsack problem, the max cut, graph, and the clique partitioning problem, the set covering problem, and the set packing problem can be derived and separated in polynomial time in this way. Our technique is algorithmic. It has been implemented and used in a set partitioning code.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/postscript
    Format: application/pdf
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    OPUS
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