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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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1

Topics in group methods for integer programming

Chen, Kenneth 15 June 2011 (has links)
In 2003, Gomory and Johnson gave two different three-slope T-space facet constructions, both of which shared a slope with the corresponding Gomory mixed-integer cut. We give a new three-slope facet which is independent of the GMIC and also give a four-slope T-space facet construction, which to our knowledge, is the first four-slope construction. We describe an enumerative framework for the discovery of T-space facets. Using an algorithm by Harvey for computing integer hulls in the plane, we give a heuristic for quickly computing lattice-free triangles. Given two rows of the tableau, we derive how to exactly calculate lattice-free triangles and quadrilaterals in the plane which can be used to derive facet-defining inequalities of the integer hull. We then present computational results using these derivations where non-basic integer variables are strengthened using Balas-Jeroslow lifting.
Lattice-free sets
T-space facets
Mixed-integer programming
Integer programming
2

Randomized integer convex hull

Hong Ngoc, Binh 12 February 2021 (has links)
The thesis deals with stochastic and algebraic aspects of the integer convex hull. In the first part, the intrinsic volumes of the randomized integer convex hull are investigated. In particular, we obtained an exact asymptotic order of the expected intrinsic volumes difference in a smooth convex body and a tight inequality for the expected mean width difference. In the algebraic part, an exact formula for the Bhattacharya function of complete primary monomial ideas in two variables is given. As a consequence, we derive an effective characterization for complete monomial ideals in two variables.
lattice polytopes
lattice-free
intrinsic volumes
mixed multiplicities
Bhattacharya function
Newton polyhedron
complete monomial ideals
mean width
random lattices
integer convex hull
random polytopes
31.70 - Wahrscheinlichkeitsrechnung
31.23 - Ideale, Ringe, Moduln, Algebren
13-02 - Research exposition
ddc:510

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