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

Christof Büskens and Helmut Maurer
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Christof Büskens: Universität Bayreuth, Lehrstuhl für Ingenieurmathematik
Helmut Maurer: Universität Münster, Institut für Numerische Mathematik

A chapter in Online Optimization of Large Scale Systems, 2001, pp 3-16 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04331-8_1

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DOI: 10.1007/978-3-662-04331-8_1

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