Mapping Efficient Numerical Methods to the Solution of Multiple Objective Linear Programs

Abstract

This investigation was initiated to increase the speed, accuracy and capacity of m-simplex algorithms for solving multiple objective linear programming problems. Specifically, improvements were sought through the application of general numerical techniques. It soon became apparent that the m- simplex algorithm, like the simplex algorithm, is heavily dependent upon the technology of solving related systems of linear equations. The numerical arguments for the application of LU triangular matrix factorization techniques to simplex computations are well known. OF special significance to m-simplex performance is the case of rank-k updates to basis factorizations. A stable and efficient LU approach to the rank-k update problem is discussed. Accompanying software supports the solution of linear and transposed constructed using BLAS and Linpack libraries.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1991
Accession Number
ADA238801

Entities

People

  • Michael A. Shields

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Algebra
  • Algorithms
  • Applied Mathematics
  • Computations
  • Computer Programming
  • Computer Programs
  • Engineering
  • Floating Point Operations
  • Linear Algebra
  • Linear Programming
  • Mathematical Programming
  • Operations Research
  • Optimization
  • Procedures (Computers)
  • Simplex Method

Readers

  • Geodesy
  • Operations Research
  • Parallel and Distributed Computing.