A Deformation Method for the Minimization of a Quadratic Function Subject to Linear Inequality Constraints

Abstract

A new method for minimizing a positive definite quadratic function subject to linear inequality constraints is presented. It is based on a continuous deformation of the quadratic starting from one giving rise to an almost trivial problem and ending with the desired quadratic. The method is particularly suitable for problems involving large numbers of inequality constraints, since the size of the variable space is independent of the number of inequalities. The method is readily extended to linear programming by embedding the linear objective function in a second degree polynomial with positive definite quadratic component, solving the resulting problem by the above method, then driving the quadratic component to zero; that is, deforming the second degree programming problem back to the original linear one.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1963
Accession Number
AD0409679

Entities

People

  • Samuel Zahl

Organizations

  • Air Force Cambridge Research Laboratories

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Coefficients
  • Computations
  • Computer Programming
  • Computers
  • Department Of Defense
  • Equations
  • Inequalities
  • Intervals
  • Linear Programming
  • Polynomials
  • Quadratic Programming
  • Random Variables
  • Terminals
  • Transitions
  • United States

Fields of Study

  • Mathematics

Readers

  • Materials Science and Engineering.
  • Operations Research

Technology Areas

  • Space