2 Optimization Use fminsearch to solve the following unconstrained optimization problem. min x∈R4 f(x) = (x1...

2 Optimization

Use fminsearch to solve the following unconstrained optimization problem. min x∈R4 f(x) = (x1 + 10x2)^2 + 5(x3 − x4)^2 + (x2 − 2x3)^4 + 10(x1 − x4)^4

Use the following as initial guess x0 = [3 -1 0 1] (x0 us a column not a row)

What is the minimizer you find, and what is the value of the objective function f(x) at that point?

Also, report the number of iterations taken to converge.

Expert Solution

the minimizer we find is [0.0094,-0.0009,0.0166,0.0166]

Minimum value is 1.3906e-06

No. of iterations 185

Colby Messinger answered 2 years ago

Solve the following problem by the dual simplex method. Min Z = 2 x1 + 3...

Solve the following problem by the dual simplex method. Min Z = 2 x1 + 3 x2 subject to 2 x1 + 2 x2 <= 30 x1 + 2 x2 >=10 x1 0, x2 >=0

Solve the following optimization problem (Be sure to include the statement of the optimization problem and...

Solve the following optimization problem (Be sure to include the statement of the optimization problem and a graph of the feasible in your solution): Jamie has joined a building contest. A dog shape requires 3 small blocks and one large block to build. A robot shape requires 5 small bricks and 5 large bricks to build. Jamie has a supply of 240 small bricks and 100 large bricks. If a dog is worth 2 points and a robot is worth...

Solve the following optimization problem. Minimize J = x + 3y + 2z

Solve the following optimization problem. MinimizeJ = x + 3y + 2zsubject to the constraints

Consider the optimization problem of the objective function f(x, y) = 3x 2 − 4y 2...

Consider the optimization problem of the objective function f(x, y) = 3x 2 − 4y 2 + xy − 5 subject to x − 2y + 7 = 0. 1. Write down the Lagrangian function and the first-order conditions. 1 mark 2. Determine the stationary point. 2 marks 3. Does the stationary point represent a maximum or a minimum? Justify your answer.

use the two-phase method and big.M method to solve the LPP: min z=x1-2x2 st: x1+x2>=2 -x1+x2>=1...

use the two-phase method and big.M method to solve the LPP: min z=x1-2x2 st: x1+x2>=2 -x1+x2>=1 x2<=3 x1,x2>=0 (two method!)

Solve the optimization problem for a Cobb-Douglas utility function with three goods: U(x1, x2, x3) =...

Solve the optimization problem for a Cobb-Douglas utility function with three goods: U(x1, x2, x3) = x c 1x d 2x f 3 , where c, d, f > 0.

Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the minimum...

Use Lagrange multipliers to solve the given optimization problem. HINT [See Example 2.] Find the minimum value of f(x, y) = x2 + y2 subject to x + 2y = 45. fmin = Also find the corresponding point (x, y). (x, y) =

Consider the following linear programming problem. min −x1 + 4x2 subject to: • x1 + x2...

Consider the following linear programming problem. min −x1 + 4x2 subject to: • x1 + x2 ≥ 1 • 3x1 + x2 ≤ .5 • x1, x2 ≥ 0 Formulate the dual of this problem.

Use MATLAB to solve the following problem: x - 3y = 2 x + 5y = 18 4x - 6y = 20

Use MATLAB to solve the following problem:x - 3y = 2x + 5y = 184x - 6y = 20

f(x) = (x^2 )0 < x < 1, (2−x), 1 < x < 2 A) Solve...

f(x) = (x^2 )0 < x < 1, (2−x), 1 < x < 2 A) Solve this integral, writing An as an expression in terms of n. Write down the values of A1,A2,A3,A4,A5 correct to 8 significant figures. b) Use MATLAB to find the coefficients of the first five harmonics and compare the results with those from part (e). Your solution should include a copy of the m-file fnc.m which you use to obtain the coefficients c) Using MATLAB, plot...

Question