Discrete relaxations of combinatorial programs

نویسندگان

  • Ralf Borndörfer
  • Robert Weismantel
چکیده

This paper investigates a technique of building up discrete relaxations of combi natorial optimization problems. To establish such a relaxation we introduce a transformation technique —aggregation— that allows one to relax an integer program by means of another integer program. We show that knapsack and set packing relaxations give rise to combinatorial cutting planes in a simple and straightforward way. The constructions are algorithmic.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Semideenite Programs and Combinatorial Optimization

Outline 1. Introductory examples: Shannon capacity and maximum cuts. 2. Preliminaries: linear programming, semideenite matrices. 3. General properties of semideenite programs: equivalent forms, Farkas Lemma, Duality Theorem, Ellipsoid method, Interior point method. 4. Getting semideenite programs I: eigenvalues of graphs and the method of variables. 5. Getting semideenite programs II: geometric...

متن کامل

Semideenite Programs and Combinatorial Optimization

Outline 1. Introductory examples: Shannon capacity and maximum cuts. 2. Preliminaries: linear programming, semideenite matrices. 3. General properties of semideenite programs: equivalent forms, Farkas Lemma, Duality Theorem, Ellipsoid method, Interior point method. 4. Getting semideenite programs I: eigenvalues of graphs and the method of variables. 5. Getting semideenite programs II: geometric...

متن کامل

A Comprehensive Analysis of Lift-and-Project Methods for Combinatorial Optimization

In both mathematical research and real-life, we often encounter problems that can be framed as finding the best solution among a collection of discrete choices. Many of these problems, on which an exhaustive search in the solution space is impractical or even infeasible, belong to the area of combinatorial optimization, a lively branch of discrete mathematics that has seen tremendous developmen...

متن کامل

Manipulating MDD Relaxations for Combinatorial Optimization

We study the application of limited-width MDDs (multivalued decision diagrams) as discrete relaxations for combinatorial optimization problems. These relaxations are used for the purpose of generating lower bounds. We introduce a new compilation method for constructing such MDDs, as well as algorithms that manipulate the MDDs to obtain stronger relaxations and hence provide stronger lower bound...

متن کامل

A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems

In this paper a reformulation technique is presented that takes a given linear zero-one programming problem, converts it into a zero-one polynomial programming problem, and then relinearizes it into an extended linear program. It is shown that the strength of the resulting reformulation depends on the degree of the terms used to produce the polynomial program at the intermediate step of this me...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 112  شماره 

صفحات  -

تاریخ انتشار 2001