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Sensitivity analysis for generalized linear-quadratic problems

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Abstract

In this paper, we study simple necessary and sufficient conditions for the stability of generalized linear-quadratic programs under perturbations of the data. The concept of generalized linear-quadratic problem was introduced by Rockafellar and Wets and consists of solving saddle points of a linear-quadratic convex concave functionJ onU×V, whereU andV are polyhedral convex sets in ℝn and ℝm. This paper also establishes results on the closedness and the uniform boundedness of the saddle-point solution sets. These properties are then used to obtain results on the continuity and the directional derivative of the perturbed saddle value.

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Authors and Affiliations

  1. Department of Mathematics, University of Paris 1, Panthéon Sorbonne, Paris, France

    A. Auslender (Professor) & P. Coutat (Graduate Student)

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  1. A. Auslender
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  2. P. Coutat
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Communicated by A. V. Fiacco

The research of the first author was supported by the CEE, Grant No. CI1-CT92-0046.

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Auslender, A., Coutat, P. Sensitivity analysis for generalized linear-quadratic problems. J Optim Theory Appl 88, 541–559 (1996). https://doi.org/10.1007/BF02192198

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