Читать книгу Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos - Страница 30

Consider the following problem:

(1.12)

Let be the global minimum of problem (1.12), and that the gradient of the equality constraints are linearly independent. In addition, assume that the corresponding Lagrange multiplier is . The vector is a perturbation vector. The solution of problem (1.12) is a function of the perturbation vector along with the multiplier. Hence, the Lagrange function can be written as

(1.13)

Calculating the partial derivative of the Lagrange function with respect to the perturbation vector, we have

(1.14)

which yields

(1.15)

Hence, the Lagrange multipliers can be interpreted as a measure of sensitivity of the objective function with respect to the perturbation vector of the constraints at the optimum point .