Answer Happy

Answer the following questions on constrained optimization problems: (a) Consider the optimization problem 1 min 36** + 2)2 + (x2 – 612 ( 1,02 s.t. x1 + 2x2 = 2. Write down the KKT conditions (or the optimality condition via the Lagrange multipliers technique) for the equality constrained problem. You may let be the Lagrange multiplier. Find a KKT point (x1, x7, \*) to the problem. (b) Consider the optimization problem 1 31,12 min 3 (81 – 3)2 + }(22 + 1)2 s.t. 2x1 + x2 > 0, x + xź < 1. Write down the KKT conditions for the above problem. You may let Mi & Ma be the slack variables corresponding to the first & second inequality, respectively. Find a KKT point (x1, x7, ui,uz) to the problem.