Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • 1995-1999  (17)
  • ddc:000  (17)
  • 1
    facet.materialart.
    Unknown
    0/1-Integer Programming: Optimization and Augmentation are Equivalent (1995)
    Details
    Publication Date: 2014-02-26
    Description: {\def\xnew{x^{\mbox{\tiny new}}}\def\Z{{{\rm Z}\!\! Z}}For every fixed set ${\cal F}\subseteq\{0,1\}^n$ the following problems are strongly polynomial time equivalent: given a feasible point $x\in\cal F$ and a linear objective function $c\in\Z^n$, \begin{itemize} \item find a feasible point $x^*\in\cal F$ that maximizes $cx$ (Optimization), \item find a feasible point $\xnew\in\cal F$ with $c\xnew〉cx$ (Augmentation), and \item find a feasible point $\xnew\in\cal F$ with $c\xnew〉cx$ such that $\xnew-x$ is ``irreducible''\\(Irreducible Augmentation). \end{itemize} This generalizes results and techniques that are well known for $0/1$--integer programming problems that arise from various classes of combinatorial optimization problems.}
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 2
    facet.materialart.
    Unknown
    Test sets and inequalities for integer programs: extended abstract (1995)
    Details
    Publication Date: 2014-02-26
    Description: This paper presents some connections between test sets and valid inequalities of integer programs. The reason for establishing such relationships is the hope that information (even partial) on one of these objects can be used to get information on the other and vice versa. We approach this study from two directions: On the one hand we examine the geometric process by which the secondary polytope associated with a matrix $A$ transforms to the state polytope as we pass from linear programs that have $A$ as coefficient matrix to the associated integer programs. The second direction establishes the notion of classes of augmentation vectors parallel to the well known concept of classes of facet defining inequalities for integer programs. We show how certain inequalities for integer programs can be derived from test sets for these programs.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 3
    facet.materialart.
    Unknown
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 4
    facet.materialart.
    Unknown
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 5
    facet.materialart.
    Unknown
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 6
    facet.materialart.
    Unknown
    Truncated Gröbner Bases for Integer Programming (1995)
    Details
    Publication Date: 2014-02-26
    Description: {\def\N{{\mbox{{\rm I\kern-0.22emN}}}}In this paper we introduce a multivariate grading of the toric ideal associated with the integer program $min \{ cx : Ax = b, x \in \N^n \}$, and a truncated Buchberger algorithm to solve the program. In the case of $max \{ cx : Ax \leq b, x \leq u, x \in \N^n \}$ in which all data are non-negative, this algebraic method gives rise to a combinatorial algorithm presented in UWZ94}.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 7
    facet.materialart.
    Unknown
    A Semidefinite Programming Approach to the Quadratic Knapsack Problem (1996)
    Details
    Publication Date: 2014-02-26
    Description: We investigate dominance relations between basic semidefinite relaxations and classes of cuts. We show that simple semidefinite relaxations are tighter than corresponding linear relaxations even in case of linear cost functions. Numerical results are presented illustrating the quality of these relaxations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 8
    facet.materialart.
    Unknown
    On Hilbert bases of polyhedral cones (1996)
    Details
    Publication Date: 2014-02-26
    Description: For a polyhedral cone $C=$ pos $\{a^1,\dots,a^m\}\subset R^d$, $a^i\in Z^d$, a subset of integral vectors $H(C)\subset C \cap Z^d$ is called a Hilbert basis of $C$ iff (i) each element of $C\cap Z^d$ can be written as a non-negative integer combination of elements of $H(C)$ and (ii) $H(C)$ has minimal cardinality with respect to all subsets of $C \cap Z^d$ for which (i) holds. We show that various problems related to Hilbert bases are hard in terms of computational complexity. However, if the dimension and the number of elements of the Hilbert basis are fixed, a Hilbert basis can always be computed in polynomial time. Furthermore we introduce a (practical) algorithm for computing the Hilbert basis of a polyhedral cone. The finiteness of this method is deduced from a result about the height of a Hilbert basis which, in particular, improves on former estimates.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 9
    facet.materialart.
    Unknown
    Quadratic Knapsack Relaxations Using Cutting Planes and Semidefinite Programming: extended abstract (1995)
    Details
    Publication Date: 2014-02-26
    Description: We investigate dominance relations between basic semidefinite relaxations and classes of cuts. We show that simple semidefinite relaxations are tighter than corresponding linear relaxations even in case of linear cost functions. Numerical results are presented illustrating the quality of these relaxations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 10
    facet.materialart.
    Unknown
    Conjunctive Cuts for Integer Programs (1998)
    Details
    Publication Date: 2014-02-26
    Description: This paper deals with a family of conjunctive inequalities. Such inequalities are needed to describe the polyhedron associated with all the integer points that satisfy several knapsack constraints simultaneously. Here we demonstrate the strength and potential of conjunctive inequalities in connection with lifting from a computational point of view.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...