ON A BRANCH-AND-BOUND METHOD FOR SEPARABLE CONCAVE PROGRAMS.

Abstract

A separable concave program is defined to be any program of the form: Minimize z(x) subject to x in K, where K is any subset of n-space and z(x) is a separable concave function, i.e. can be written as a sum of n concave functions each of which depends on only one of the components of the vector x. (A familiar special case is the so-called fixed charge linear program.) It is shown how a branch-and-bound algorithm for a separable concave program can always be obtained if the related program of minimizing a linear function over K can be performed efficiently. A special case is considered in which K is a very large discrete set but can be described as the vector sum of smaller sets. The branch-and-bound algorithm for this special case has been programmed and applied to a problem of selecting a minimum cost fleet of space vehicles. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1967
Accession Number
AD0663680

Entities

People

  • D. W. Walkup

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Evolutionary Algorithms
  • Heuristic Methods
  • Linear Programming
  • Mathematics
  • Simplex Method
  • Spacecraft
  • Vehicles

Fields of Study

  • Mathematics

Readers

  • Operations Research

Technology Areas

  • Space