= 3. (25 points] Consider the following primal problem: min f(x) = -(x1 4)2...
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= 3. (25 points] Consider the following primal problem: min f(x) = -(x1 4)2 (x2 4)2 s.t. 91(x) = 21-30 0). = The dual problem is max 0(u) s.t. u > 0 where 0(U1, U2) = min{-(x1 4)2 (x2 4)2 + u1(x1 3) + u2(-x1 + x2 2) : x X}. = > = (3; 7). (a) Find the steepest ascent direction of 0 at u(0) (b) Do the exact line search to find u(1) > 0. = 3. (25 points] Consider the following primal problem: min f(x) = -(x1 4)2 (x2 4)2 s.t. 91(x) = 21-30 0). = The dual problem is max 0(u) s.t. u > 0 where 0(U1, U2) = min{-(x1 4)2 (x2 4)2 + u1(x1 3) + u2(-x1 + x2 2) : x X}. = > = (3; 7). (a) Find the steepest ascent direction of 0 at u(0) (b) Do the exact line search to find u(1) > 0
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