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Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems

  • Christof Büskens
  • Helmut Maurer
Chapter

Abstract

Basic results for sensitivity analysis of parametric nonlinear programming problems [11] are revisited. Emphasis is placed on those conditions that ensure the differentiability of the optimal solution vector with respect to the parameters involved in the problem. We study the explicit formulae for the sensitivity derivatives of the solution vector and the associated Lagrange multipliers. Conceptually, these formulae are tailored to solution algorithm calculations. However, we indicate numerical obstacles that prevent these expressions from being a direct byproduct of current solution algorithms. We investigate post-optimal evaluations of sensitivity differentials and discuss their numerical implementation. The main purpose of this paper is to describe an important application of sensitivity analysis: the development of real-time approximations of the perturbed solutions using Taylor expansions. Two elementary examples illustrate the basic ideas.

Keywords

Sensitivity Differential Order Taylor Expansion Sensitivity Derivative Sensitivity Domain Second Order Sufficient Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Christof Büskens
    • 1
  • Helmut Maurer
    • 2
  1. 1.Lehrstuhl für IngenieurmathematikUniversität BayreuthGermany
  2. 2.Institut für Numerische MathematikUniversität MünsterGermany

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