Perturbation Approach to Sensitivity Analysis in Mathematical Programming

E. Castillo, A. J. Conejo, C. Castillo, R. Mínguez and D. Ortigosa
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E. Castillo: University of Cantabria
A. J. Conejo: University of Castilla-La Mancha
C. Castillo: University of Granada
R. Mínguez: University of Castilla-La Mancha
D. Ortigosa: University of La Rioja

Journal of Optimization Theory and Applications, 2006, vol. 128, issue 1, No 3, 49-74

Abstract: Abstract This paper presents a perturbation approach for performing sensitivity analysis of mathematical programming problems. Contrary to standard methods, the active constraints are not assumed to remain active if the problem data are perturbed, nor the partial derivatives are assumed to exist. In other words, all the elements, variables, parameters, Karush–Kuhn–Tucker multipliers, and objective function values may vary provided that optimality is maintained and the general structure of a feasible perturbation (which is a polyhedral cone) is obtained. This allows determining: (a) the local sensitivities, (b) whether or not partial derivatives exist, and (c) if the directional derivative for a given direction exists. A method for the simultaneous obtention of the sensitivities of the objective function optimal value and the primal and dual variable values with respect to data is given. Three examples illustrate the concepts presented and the proposed methodology. Finally, some relevant conclusions are drawn.

Keywords: Local sensitivity; mathematical programming; duality; polyhedral cones (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s10957-005-7557-y

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