Generalized Equations and Their Solutions. Part I. Basic Theory.

Abstract

A class of 'generalized equations,' involving point-to-set mappings, which formulate the problems of linear and nonlinear programming and of complementarity, among others, has been considered. Solution sets of such generalized equations are shown to be stable under certain hypotheses; in particular a general form of the implicit function theorem is proved for such problems. An application to linear generalized equations is given at the end of the paper; this covers linear and convex quadratic programming and the positive semidefinite linear complementarity problem. The general nonlinear programming problem is treated in Part II of the paper, using the methods developed here.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1977
Accession Number
ADA049495

Entities

People

  • Stephen M. Robinson

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Computer Programming
  • Convex Sets
  • Equations
  • Hypotheses
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Operations Research
  • Optimization
  • Quadratic Programming
  • Systems Engineering
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research