Develop your own Matlab$/$Python code to solve a complete unconstrained nonlinear optimization problem such that your code should be able to switch to first order and QuasiNewton methods for search direction determination using

a$)$ Steepest Descent Method

b$)$ Conjugate Gradient Method

c$)$ Davidon$-$Fletcher$-$Powell $($DFP$)$ Method

d$)$ Broyden$-$Fletcher$-$Goldfarb$-$Shanno $($BFGS$)$ Method

Requirements:

Please note that:

For determination of the optimum step size ${}^{**}$ of change in design $vec(x),$ use the Golden Section Search Method code that you have developed in Homework $3$

You can use central finite differencing to calculate the gradients or get the derivatives analytically.

Verify your code with the solved exercises in your textbook.

Next, solve the following optimization problem with the $3$ methods above, using your own code.

minf$(vec(x))=a**x_1^2+2**(b+j)**x_2^2-4**f**x_1-2**h**x_1{x}_2$

starting with initial design at $(1,1).$

Where you will use your university student id number to determine a$,$b$,$c$,$d$,$e$,$f$,$g$,$h$,$j$.$ Your number is $[$abcdefghj$].$

Compare the accuracy of the optimum results and the convergence rate $($in terms of number of function evalutaions and iterations$)$ of all $4$ methods.

$($Use a series type plot to compare convefrgence rates$).$ Show all the iteration values of the design variables.

Please submit

a$)$ Soft copy of your Matlab$/$ Python program $($no bugs$)$ Your code must run without errors.

b$)$ A technical paper of your work $($clear$,$ fluent, complete, understandable, must have formulations, flowchart and a good discussion$).$ Please use AIAA class template for your report.

c$)$ Submit your homework to Ninova. No emails will be accepted. There will be no extensions.