Improved Convexity Cuts for Lattice Point Problems

Abstract

The generalized lattice point (GLP) problem provides a formulation that accommodates a variety of discrete alternative problems. In the paper the authors show how to substantially strengthen the convexity cuts for the GLP problem. The new cuts are based on the identification of synthesized lattice point conditions to replace those that ordinarily define the cut. The synthesized conditions give an alternative set of hyperplanes that enlarge the convex set, thus allowing the cut to be shifted deeper into the solution space. A convenient feature of the strengthened cuts is the existence of linking relationships by which they may be constructively generated from the original cuts. Geometric examples are given in the last section to show how the new cuts improve upon those previously proposed for the GLP problem.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1973
Accession Number
AD0763385

Entities

People

  • Darwin Dee Klingman
  • Fred W. Glover

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Commerce
  • Computer Programming
  • Computer Science
  • Convex Programming
  • Convex Sets
  • Integer Programming
  • Linear Programming
  • Mathematical Programming
  • Military Research
  • Operations Research
  • Simplex Method
  • Theorems
  • United States
  • United States Government
  • Universities

Readers

  • Operations Research
  • Theoretical Analysis.

Technology Areas

  • Space