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In this paper we consider a semidefinite programming (SDP) problem in which the objective function depends linearly on a scalar parameter. We study the properties of the optimal objective function value as a function of that parameter and extend the concept of the optimal partition and its range in linear programming to SDP. We also consider an approach to sensitivity analysis in SDP and the extension of our results to an SDP problem with a parametric right-hand side.
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Goldfarb et al. (1999) studied this question.
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