Lipschitz Continuity of Solutions of Linear Inequalities, Programs and Complementarity Problems.

Abstract

It is shown that solutions of linear inequalities, linear programs and certain linear complementarity problems (e.g. those with P-matrices or Z-matrices but not semidefinite matrices) are Lipschitz continuous with respect to changes in the right hand side data of the problem. Solutions of linear programs are not Lipschitz continuous with respect to the coefficients of the objective function. The Lipschitz constant given here is a generalization of the role played by the norm of the inverse of a nonsingular matrix in bounding the perturbation of the solution of a system of equations in terms of a right hand side perturbation. Keywords: Optimization. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1985
Accession Number
ADA160957

Entities

People

  • Olvi L. Mangasarian
  • T. H. Shiau

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Classification
  • Coefficients
  • Computer Programming
  • Continuity
  • Contracts
  • Equations
  • Inequalities
  • Intervals
  • Linear Programming
  • Materials
  • Mathematics
  • North Carolina
  • Optimization
  • Perturbations
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research