The question is about convex NLPS and KKT conditions, which I do not quite understand. I just want to know that how to write the optimality conditions for x bar in the KKT and prove x bar is an optimal solution in question a, and also show that constraint 3 is tight at x' . Thank you for your help.

Question 5. Convex NLPs and KKT conditions (15 marks) Consider the following non-linear program. min 333 (NLP) 8.1}. 1'1 + 1172 S 0 (1) sf 4 s 0 (2) wf2x1+xm3+1_<_0. you may assume without proof that is a convex non-linear program. consider the point write down optimality conditions for lp as described in karushkuhntucker theorem. using these and theorem prove if an optimal solution. marks show any solution to it must be that: constraint tight at w>