Introduction to Optimum Design, 2nd Edition

4.5 Postoptimality Analysis: Physical Meaning of Lagrange Multipliers

The study of variations in the optimum solution as some of the original problem parameters are changed is known as postoptimality analysis or sensitivity analysis. This is an important topic for optimum design of engineering systems. Variation of the optimum cost function and design variables due to the variations of many parameters can be studied. Since sensitivity of the cost function to the variations in the constraint limit values can be studied without any further analysis, we shall focus on this aspect of sensitivity analysis only. We shall assume that the minimization problem has been solved with h_i(x) = 0 and g_j(x) ≤ 0, i.e., with the current limit values for the constraints ...