Homework Answers
clc;
clear all;
h=0.01;
x=[0:h:5];
s=length(x);
for i=1:s
if x(i)<=3
y(i)=-x(i)+4;
else
y(i)=(x(i)-2)^2;
end
end
plot(x,y)
m=max(y)
m=9
Add Answer to:
Consider the following function over real variable x: r = 1 -x + 4 ((x -...
Consider the following optimization problem: minimize 71 subject tox,- r, where r > 0 is a given scalar 1. Write dow...
Consider the following optimization problem: minimize 71 subject tox,- r, where r > 0 is a given scalar 1. Write down the FONC and SONC for this problem. (5 points) 2. Shw ihai whken f is vx, nxxssary conditions a: also sufiint. (10 poimis)
Consider the following optimization problem: minimize 71 subject tox,- r, where r > 0 is a given scalar 1. Write down the FONC and SONC for this problem. (5 points) 2. Shw ihai whken f is...
6.5 A simple example of an optimization method is the random search method. This method repeatedly...
6.5 A simple example of an optimization method is the random search method. This method repeatedly evaluates the function at randomly selected values of the optimization variables. If a sufficient number of samples are conducted, the optimum would eventually be found. Consider the optimization problem min f(x,y) = -8x + x2 +12y + 4y2 – 2xy x,y a. Write down the step-to-step algorithm you would use to solve the problem. b. Implement your algorithm in MATLAB to solve the problem....
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6?...
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6? + 10 a. Write a Python function for the derivative of f(x) that takes x and returns the derivative of f(x). Take the derivative of f(x) analytically with respect to x before writing the function. b. Write a Python code that approximately finds the real root, x0, of f(x) such that f(x0)~0 using the Newton-Raphson method. The code is expected to get an initial...
Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: ...
This is a MATLAB question so please answer them with MATLAB
steps.
Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: use the roots command. 3. Find the global minimum for f(x). Hint: plot f over [0,2] 4. Solve f()P. Hint: plot f and P over [0,21. 5. Find lim,→0+ f(x). Hint: make a vector hi make a table [x + h; f(x + h)]". 6. Find '(In 2)....
matlab only Question 5: a.) Write an m-file using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function is for x <-1 - 3e y=2...
matlab only
Question 5: a.) Write an m-file using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function is for x <-1 - 3e y=2+cos(m) for-1 x<5 y 10-5)+1 for r 2 5 Use your file to evaluate y for x5, x-3, and x-15, and Use keyboard entry for values of x. b.) Use a for loop in the above file to plot the above function over the interval -2x <10....
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that...
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that the function can be extended and modelled as a Fourier cosine-series: (a) Sketch this extended function in the interval that satisfies: x <4 (b) State the minimum period of this extended function. (C) The general Fourier series is defined as follows: [1 marks] [1 marks] F(x) = 4 + ] Ancos ("E") + ] B, sin("E") [1 marks] State the value of L. (d)...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment p...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
Consider the following linear regression model 1. For any X x, let Y xBU, where 3...
Consider the following linear regression model 1. For any X x, let Y xBU, where 3 E R*. 2. X is exogenous 3. The probability model is {f(u;0) is a distribution on R: Ef [U] = 0, VAR, [U] = 02,0 > 0}. 4. Sampling model: Y} anidependent sample, sequentially generated using Yi x Ui,where the U IID(0,0) are (i) Let K 0 be a given number. We wish to estimate B using least-squares subject to the constraint 6BK2. Write...
code in Matlab Problem 1: The MATLAB humps function defines a curve that has 2 maxima (peaks) of unequal height over the interval 0 2, f(x) = r-0.3)2 +0.01 (r-09 +0.04 Use MATLAB to generate a plo...
code in Matlab
Problem 1: The MATLAB humps function defines a curve that has 2 maxima (peaks) of unequal height over the interval 0 2, f(x) = r-0.3)2 +0.01 (r-09 +0.04 Use MATLAB to generate a plot of Kx) versus x with x [0:1/256:2: Do not use MATLAB's built-in humps function to generate the values of Rx). Also, employ the minimum number of periods to perform the vector operations needed to eneate x) values for the plo
Problem 1: The...
(4) Let f R -R be a strictly conve:r C2 function and let 0 a) Write the Euler-Lagrange equation...
(4) Let f R -R be a strictly conve:r C2 function and let 0 a) Write the Euler-Lagrange equation for the minimizer u.(x) of the following problem: minimize u subject to: u E A, where A- 0,REC1[0 , 1and u (0 a u(1)b) b) Assuming the minimizer u(a) is a C2 function, prove t is strictly convex
(4) Let f R -R be a strictly conve:r C2 function and let 0
a) Write the Euler-Lagrange equation for the minimizer u.(x)...
Consider the following optimization problem: minimize 71 subject tox,- r, where r > 0 is a given scalar 1. Write down the FONC and SONC for this problem. (5 points) 2. Shw ihai whken f is vx, nxxssary conditions a: also sufiint. (10 poimis)
Consider the following optimization problem: minimize 71 subject tox,- r, where r > 0 is a given scalar 1. Write down the FONC and SONC for this problem. (5 points) 2. Shw ihai whken f is...
6.5 A simple example of an optimization method is the random search method. This method repeatedly evaluates the function at randomly selected values of the optimization variables. If a sufficient number of samples are conducted, the optimum would eventually be found. Consider the optimization problem min f(x,y) = -8x + x2 +12y + 4y2 – 2xy x,y a. Write down the step-to-step algorithm you would use to solve the problem. b. Implement your algorithm in MATLAB to solve the problem....
This is a MATLAB question so please answer them with MATLAB
steps.
Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: use the roots command. 3. Find the global minimum for f(x). Hint: plot f over [0,2] 4. Solve f()P. Hint: plot f and P over [0,21. 5. Find lim,→0+ f(x). Hint: make a vector hi make a table [x + h; f(x + h)]". 6. Find '(In 2)....
matlab only
Question 5: a.) Write an m-file using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function is for x <-1 - 3e y=2+cos(m) for-1 x<5 y 10-5)+1 for r 2 5 Use your file to evaluate y for x5, x-3, and x-15, and Use keyboard entry for values of x. b.) Use a for loop in the above file to plot the above function over the interval -2x <10....
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that the function can be extended and modelled as a Fourier cosine-series: (a) Sketch this extended function in the interval that satisfies: x <4 (b) State the minimum period of this extended function. (C) The general Fourier series is defined as follows: [1 marks] [1 marks] F(x) = 4 + ] Ancos ("E") + ] B, sin("E") [1 marks] State the value of L. (d)...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
Consider the following linear regression model 1. For any X x, let Y xBU, where 3 E R*. 2. X is exogenous 3. The probability model is {f(u;0) is a distribution on R: Ef [U] = 0, VAR, [U] = 02,0 > 0}. 4. Sampling model: Y} anidependent sample, sequentially generated using Yi x Ui,where the U IID(0,0) are (i) Let K 0 be a given number. We wish to estimate B using least-squares subject to the constraint 6BK2. Write...
code in Matlab
Problem 1: The MATLAB humps function defines a curve that has 2 maxima (peaks) of unequal height over the interval 0 2, f(x) = r-0.3)2 +0.01 (r-09 +0.04 Use MATLAB to generate a plot of Kx) versus x with x [0:1/256:2: Do not use MATLAB's built-in humps function to generate the values of Rx). Also, employ the minimum number of periods to perform the vector operations needed to eneate x) values for the plo
Problem 1: The...
(4) Let f R -R be a strictly conve:r C2 function and let 0 a) Write the Euler-Lagrange equation for the minimizer u.(x) of the following problem: minimize u subject to: u E A, where A- 0,REC1[0 , 1and u (0 a u(1)b) b) Assuming the minimizer u(a) is a C2 function, prove t is strictly convex
(4) Let f R -R be a strictly conve:r C2 function and let 0
a) Write the Euler-Lagrange equation for the minimizer u.(x)...
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