5.9 Draw an x1,x2 coordinate system and show the convex region which satisfies the constraints that...
x1.x2 Subject to 4x1-3x2 S 20 x1 +2x2 s 10 a) Is this problem convex? Justify your answer. (5 Points) b) Form the Lagrangian function. (5 Points) c) Formulate KKT conditions. (10 Points) d) Recall that one technique for finding roots of KKT condition is to check all permutations of the switching conditions. Find an optimal solution (x*) via e) Compute the objective function and identify each constraint as active or f) Solve this problem using graphical optimization to check...
(45 Points) Consider the constrained optimization problem: min f(x1, x2) = 2x} + 9x2 + 9x2 - 6x1x2 – 18x1 X1 X2 Subject to 4x1 – 3x2 s 20 X1 + 2x2 < 10 -X1 < 0, - x2 < 0 a) Is this problem convex? Justify your answer. (5 Points) b) Form the Lagrange function. (5 Points) c) Formulate KKT conditions. (10 Points) d) Recall that one technique for finding roots of KKT condition is to check all permutations...
7 points Question 3. An Unusual Integrable Function (Show Working) Consider the function f : 10, 11 → R defined by 1 if r-for some nEN; f(x) = 0 for all other x E [0,1 (1 subpts) (a) Draw a rough diagram of the graph of f. When we study the formal definition of the continuity of a function later in the course, we will be able to prove that this function is discontinuous at those domain values r such...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...