Generalized Equations and Their Solutions. Part 2. Applications to Nonlinear Programming

Abstract

We prove that if the second-order sufficient condition and constraint regularity hold at a local minimizer of a nonlinear programming problem, then for sufficiently smooth perturbations of the constraints and objective function the set of local stationary points is nonempty and continuous; further, if certain polyhedrality assumptions hold (as is usually the case in applications) then the local minimizers, the stationary points and the multipliers all obey a type of Lipschitz condition. Through the use of generalized equations, these results are obtained with a minimum of notational complexity.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1980
Accession Number
ADA086365

Entities

People

  • Stephen M. Robinson

Organizations

  • University of Wisconsin–Madison

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DTIC Thesaurus Topics

  • Applied Mathematics
  • Chemical Engineering
  • Convex Sets
  • Engineering
  • Equations
  • Hypotheses
  • Inequalities
  • Mathematical Analysis
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Numerical Analysis
  • Operations Research
  • Perturbations
  • Standards
  • Theorems
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Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research