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

In: Online Optimization of Large Scale Systems

Author

Listed:
  • Christof Büskens

    (Universität Bayreuth, Lehrstuhl für Ingenieurmathematik)

  • Helmut Maurer

    (Universität Münster, Institut für Numerische Mathematik)

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.

Suggested Citation

  • Christof Büskens & Helmut Maurer, 2001. "Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems," Springer Books, in: Martin Grötschel & Sven O. Krumke & Jörg Rambau (ed.), Online Optimization of Large Scale Systems, pages 3-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04331-8_1
    DOI: 10.1007/978-3-662-04331-8_1
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