Extensions of the Gauvin-Tolle Optimal Value Differential Stability Results to General Mathematical Programs.

Abstract

Gauvin and Tolle have obtained bounds on the directional derivative limit quotient of the optimal value function for mathematical programs containing a right-hand side perturbation. In this paper, we extend the results of Gauvin and Tolle to the general mathematical program in which a parameter appears arbitrarily in the constraints and in the objective function. An implicit function theorem is applied to transform the general mathematical program to a locally equivalent inequality constrained program, and, under conditions used by Gauvin and Tolle, their upper and lower bounds on the optimal value function directional derivative limit quotient are shown to pertain to this reduced program. These bounds are then shown to apply in programs having both inequality and equality constraints where a parameter may appear anywhere in the program. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 20, 1979
Accession Number
ADA071746

Entities

People

  • Anthony V. Fiacco
  • William P. Hutzler

Organizations

  • George Washington University

Tags

Communities of Interest

  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computer Programming
  • Continuity
  • Convex Programming
  • Directional
  • Engineering
  • Evolutionary Algorithms
  • Hypotheses
  • Inequalities
  • Linear Programming
  • Mathematical Programming
  • Military Research
  • Nonconvex Programming
  • Nonlinear Programming
  • Numbers
  • Operations Research
  • Optimization
  • Systems Engineering

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Emergency Management and Homeland Security.