$-$ Use Matlab or python as the programming language.

$-$ Initial solution is set to be the vector of zeros, i$.$e$.\backslash (\backslash$mathbf$\{$w$\}\_\{0\}=\backslash$mathbf$\{0\}\backslash ).$

$-$ The algorithm stops when the maximum iteration $(1000)$ is hit

$-$ Fix the step size to be $\backslash (\backslash$frac$\{0\mathrm{.}85\}\{$k$\}\backslash ),$ where $\backslash ($ k $\backslash )$ is the number of iterations

$-$ You should try to write your code in an efficient way, resulting in a runtime that does not exceed $5$ minutes for each algorithm.

$3.(10$ marks.$)$ Program the steepest descent algorithm with fixed step size to minimize $\backslash ($ l $\backslash ).$ Plot the objective function as a function of number of iterations.

$4.(10$ marks.$)$ Program the stochastic gradient descent algorithm with fixed step size to minimize $\backslash ($ l $\backslash ).$ Plot the objective function as a function of number of iterations.