Analytically, find the optimum solutions and optimum function variable to the fo

Question

Analytically, find the optimum solutions and optimum function variable to the following optimization problem. min x,y f(x,y)=(x-2)^2+(y+1)^2 subject to: 2x + 3y - 4 = 0 7. Using Matlab's built in "fmincon" command, study the common wine bottle function: f(x_1,x_2) = c+1/9.32 Where: c = a^2+b^2+3/2 + sin(a^2 + b^2+2) a = 6x_1 - 3 b = 6x_2 - 3 0 x_1,x_2 1 A series of local minimums can be found. a) Plot the function surface to get an idea of where the local minimums should be b) Solve the optimization problem 1,000 times using random initial guesses c) Plot all 1,000 solutions on a graph with axis x_1 and X_2

Explanation / Answer

6)

using analytical approach we can have minimum of both the squares at x=2 and y=-1.

With x=2 the solution will be minimum

now 2x+3y-4=0

if x=2 then y=0

the minimum value of function will be 1.

7)

the local minimum based on the condition will be at x1==0.5 and x2=0.5

We can use matlab to plot the same graph using fmincon function.

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