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symmetric cones
Multi-parametric sensitivity analysis of the constraint matrix in
piecewise linear fractional programming
In this paper, we study multi-parametric sensitivity analysis for
programming
problems with the piecewise linear fractional objective function using the
concept of maximum volume in the tolerance
region. We construct critical regions (the set of parameters values which the coefficients matrix of the problem (PLFP) may vary while still retaining the same optimal basis B.) for simultaneous and
independent perturbations of one row or one column of the constraint matrix in the given problem. Necessary
and sufficient conditions are derived to classify perturbation parameters as
'focal' and 'non-focal'. Non-focal parameters can be deleted from
the analysis, because of their low sensitivity in practice.
Theoretical results are illustrated with the help of a numerical
example.