Inversion of Perturbed Matrix: The Key Step towards Generic Parametric Programming

Parametric optimization with uncertainties on the objective function (OF) or on the so-called “right-hand-side” (RHS) of the constraints has been successfully addressed in recent years. However, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. This gap in the research exists even though there are numerous real industrial problems where the LHS parameters are subject to some uncertainties.

When the uncertainty is on the RHS or OF, we deal with a vector of uncertain parameters. However, if the uncertainty is on the LHS, the problem is a parametric matrix which is one of the complex mathematical problems. In this presentation, we will introduce an algorithm for a linear program with a multicomponent single parameter on the left hand side [1].

[1] KHALILPOUR, R., Parametric Optimization with Uncertainty on the Left Hand Side, July 2007, Research Report, Singapore: National University of Singapore.