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)

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.