1. Consider a general constrained optimization problem min f(x) xƐR" s.t. c;(x) = 0, i e E, G(x) > 0, i E I. a. Write Lagrangian function for this problem. b. Write KKT conditions corresponding to...

0, i E I. a. Write Lagrangian function for this problem. b. Write KKT conditions corresponding to this problem. c. Prove that when the KKT conditions and the LICQ are satisfied at a point a*, the Lagrange multiplier X* is unique. "/>
Extracted text: 1. Consider a general constrained optimization problem min f(x) xƐR" s.t. c;(x) = 0, i e E, G(x) > 0, i E I. a. Write Lagrangian function for this problem. b. Write KKT conditions corresponding to this problem. c. Prove that when the KKT conditions and the LICQ are satisfied at a point a*, the Lagrange multiplier X* is unique.