-

 

 

 




Optimization Online





 

Scanning integer points with lex-cuts: A finite cutting plane algorithm for integer programming with linear objective

Michele Conforti (conforti***at***math.unipd.it)
Marianna De Santis (mdesantis***at***diag.uniroma1.it)
Marco Di Summa (disumma***at***math.unipd.it)
Francesco Rinaldi (rinaldi***at***math.unipd.it)

Abstract: We consider the integer points in a box B ordered by a lexicographic rule defined by a lattice basis. To each integer point x in B we associate a cutting plane (lex-cut) that eliminates the integer points in B that are lexicographically smaller than x and is satisfied by the others. The family of lex-cuts contains the Chvatal-Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program min{cx: x \in S \cap Z^n}, where S \subset R^n is a compact set and c \in Z^n. We analyze the worst-case behavior of our algorithm and propose some variants.

Keywords: Integer Nonlinear Programming, Cutting plane algorithm

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation:

Download: [PDF]

Entry Submitted: 07/25/2018
Entry Accepted: 07/25/2018
Entry Last Modified: 11/05/2018

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society