Question: Sensitivity Analysis: Nonlinear Optimization. Unlike the shadow prices of a linear program, the Lagrange multipliers of a nonlinear program generally only give an ap- proximation

Sensitivity Analysis: Nonlinear Optimization. Unlike the shadow prices of a linear program, the Lagrange multipliers of a nonlinear program generally only give an ap- proximation of the change in the optimal objective value. Consider the following NLP: min 1 + 2 + 13 s.t. x1 + x2 = 3 X1 + 312 + 213 = 7 (a) Find all points satisfying the first order necessary conditions. (b) Which of the points from part (a) can be classified as local minimizers according to the second order sufficiency conditions. (c) Suppose the right hand side of the first constraint changes from 3 to 4. Use the Lagrange multiplier to estimate the change in the objective function. Then calculate the true optimal solution (feel free to use software to do this) and discuss the accuracy of your estimate. (d) (independent of part (c)) Suppose the right hand side of the first constraint changes from 3 to 6. Use the Lagrange multiplier to estimate the change in the objective function. Then calculate the true optimal solution (feel free to use software to do this) and discuss the accuracy of your estimate

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