Lipschitz Properties of Solution in Mathematical Programming.

Abstract

In this paper, we are concerned with the behaviour of the solutions of problems and also with the Lipschitzian dependence of the set of solutions with respect to the parameter alpha. The paper is organized as follows. The main theorems of the paper are stated. Sufficient conditions are give to have (1) local uniqueness of solutions and (2) Lipschitzian dependence of the solution with respect to the parameter alpha. The proofs of the theorems are given. The main tool, in this analysis, is an implicit function theorem for Lipschitzian mappings due to Clarke (see also Hiriart-Urruty). The main idea is to write the generalized equation as a system of Lipschitzian mapping, to which Clarke's implicit function can be applied. The notion of generalized derivative of the projection mapping on a convex are of particular use.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1982
Accession Number
ADA121740

Entities

People

  • Bernard Cornet
  • Guy Laroque

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Computations
  • Computer Programming
  • Equations
  • Inequalities
  • Mathematical Programming
  • Mathematics
  • Military Research
  • New York
  • Nonlinear Programming
  • Operations Research
  • Perturbation Theory
  • Sequences
  • Social Sciences
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Materials Science (Mechanical Engineering).
  • Operations Research