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1. (15 points) Let f(x1, x2) = q*i-3x2 + e*1 +372 +e-1. Starting with (0,0), determine...
Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0)...
Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0) exists. which
Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0) exists. which
1. [10 marks) Let X, and X, have joint density function f(0,0%) = cca 110, x2...
1. [10 marks) Let X, and X, have joint density function f(0,0%) = cca 110, x2 > 0,8 +29 < 1, where c is a constant. Find: (a) (2 marksThe value of c. (b) (2 marks] E(XX). (c) (2 marks] P(X1 < 3X2). (a) (2 marks] (2016). (e) (2 marks] E(X1/X3 = 5).
5. Let f(x) = ax2 +bx+c, where a > 0. Prove that the secant method for...
5. Let f(x) = ax2 +bx+c, where a > 0. Prove that the secant method for minimization will terminate in exactly one iteration for any initial points Xo, X1, provided that x1 + xo: 6. Consider the sequence {x(k)} given by i. Write down the value of the limit of {x(k)}. ii. Find the order of convergence of {x(k)}. 7. Consider the function f(x) = x4 – 14x3 + 60x2 – 70x in the interval (0, 2). Use the bisection...
(45 Points) Consider the constrained optimization problem: min f(x1, x2) = 2x} + 9x2 + 9x2...
(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...
Let f(1 , Τρ, T3) (x1+x , (x1, x2, T3) E R3, a > 0. For...
Let f(1 , Τρ, T3) (x1+x , (x1, x2, T3) E R3, a > 0. For which a is the function f differentiable at 0?
Let f(1 , Τρ, T3) (x1+x , (x1, x2, T3) E R3, a > 0. For which a is the function f differentiable at 0?
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of...
Write neatly please =)
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
5. Let F = (3x2 + 2xy + y2)i + (x2 + 2xy + 4y3)j, and...
5. Let F = (3x2 + 2xy + y2)i + (x2 + 2xy + 4y3)j, and let C be any curve in R2 which begins at the origin and ends at (1, 2). Find ( F.dr.
min (x2 - 2 x1)4 + 64 xj x2 XER and the points a = (1,5),...
min (x2 - 2 x1)4 + 64 xj x2 XER and the points a = (1,5), b = (0,0)", c= (1,-1)", d= (-3,1) Select all true statements from the options below: TESCO give ... score for this problem may be smaller than the actual one after we added partial credits Od is a global minimizer Othere is only one global minimizer cis a strict local minimizer Od is a strict local minimizer the objective function is coercive Ob is a...
, to solve the equation set Given x=ly. I, L4」 f(x) Lf,(x)」"[x2-4-1」 , f(x)-0, with an initial...
, to solve the equation set Given x=ly. I, L4」 f(x) Lf,(x)」"[x2-4-1」 , f(x)-0, with an initial guess of x"-0, ie. , xi (0)-0 x2 (0)-0. a Using the Jacobian methods, determine the iteration unction, and the estimate value of x = x1 (b) Using the Newton-Raphson approach, determine the iteration function, and the estimate value of x2 after first two iterations, show the work. x=[x1,x2lT after first iteration. fa * Hint: the inverse ofa 2-dimension matrix: 1Ta b -b...
Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0) exists. which
Let f(x, 2) Va r], (x1, X2) E R2. Determine all directions E R2 along (0,0) exists. which
1. [10 marks) Let X, and X, have joint density function f(0,0%) = cca 110, x2 > 0,8 +29 < 1, where c is a constant. Find: (a) (2 marksThe value of c. (b) (2 marks] E(XX). (c) (2 marks] P(X1 < 3X2). (a) (2 marks] (2016). (e) (2 marks] E(X1/X3 = 5).
5. Let f(x) = ax2 +bx+c, where a > 0. Prove that the secant method for minimization will terminate in exactly one iteration for any initial points Xo, X1, provided that x1 + xo: 6. Consider the sequence {x(k)} given by i. Write down the value of the limit of {x(k)}. ii. Find the order of convergence of {x(k)}. 7. Consider the function f(x) = x4 – 14x3 + 60x2 – 70x in the interval (0, 2). Use the bisection...
(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...
Let f(1 , Τρ, T3) (x1+x , (x1, x2, T3) E R3, a > 0. For which a is the function f differentiable at 0?
Let f(1 , Τρ, T3) (x1+x , (x1, x2, T3) E R3, a > 0. For which a is the function f differentiable at 0?
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
Write neatly please =)
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
5. Let F = (3x2 + 2xy + y2)i + (x2 + 2xy + 4y3)j, and let C be any curve in R2 which begins at the origin and ends at (1, 2). Find ( F.dr.
min (x2 - 2 x1)4 + 64 xj x2 XER and the points a = (1,5), b = (0,0)", c= (1,-1)", d= (-3,1) Select all true statements from the options below: TESCO give ... score for this problem may be smaller than the actual one after we added partial credits Od is a global minimizer Othere is only one global minimizer cis a strict local minimizer Od is a strict local minimizer the objective function is coercive Ob is a...
, to solve the equation set Given x=ly. I, L4」 f(x) Lf,(x)」"[x2-4-1」 , f(x)-0, with an initial guess of x"-0, ie. , xi (0)-0 x2 (0)-0. a Using the Jacobian methods, determine the iteration unction, and the estimate value of x = x1 (b) Using the Newton-Raphson approach, determine the iteration function, and the estimate value of x2 after first two iterations, show the work. x=[x1,x2lT after first iteration. fa * Hint: the inverse ofa 2-dimension matrix: 1Ta b -b...
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