Sensitivity analysis

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The concern with how the solution changes if some changes are made in either the data or in some of the solution values (by fixing their value). Marginal analysis is concerned with the effects of small perturbations, maybe measurable by derivatives. Parametric analysis is concerned with larger changes in parameter values that affect the data in the mathematical program, such as a cost coefficient or resource limit.

Under suitable assumptions, the multipliers in the Lagrange Multiplier Rule provide derivatives of the optimal response function – i.e., under certain conditions, LaTeX: \textstyle (u, v) = \nabla f^* (b, c). For special approaches in LP, see compatibility theory, the 100% Rule, and the tolerance approach.

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