Estimate the global optima

Two objective functions are used in this project.

has the minimum when $x=3.$

Eq$.(1)$

$f(x)=60si{n}^2(x)+x^2,f(x)$ has the minimum when $x=0.$

Eq$.(2)$

Those two objective functions have multiple local minima and one global minimum, shown in Fig. $4$ and Fig. $5.$

$3.$ Project report

In your project report, you need to provide:

Source code written by Python language, which estimates the global optima of Eq$.(1)$ and Eq$.(2).$

The global optima and the corresponding horizontal coordinates.

Time consumption in seconds $($Running time$)$ when searching the global optima.

Submit your project report to Blackboard

Project $1.$

$1.$Design a Python program based on the following pseudo code.

Tab $1.$ An algorithm, which is able to find out the global optima

Initialize $x_1=-6,x_2=6$;

Initialize $T_0=0\mathrm{.}01$;

Initialize $T_k=0\mathrm{.}01$;

Initialize $x_0$;

Initialize the step size $S=1$;

Initialize $x_{\text{o}\text{p}\text{t}\text{i}\text{m}\text{a}\text{l}}=0$;

Define an objective function $f(x)$;

Initialize $x=$random$(x_1,x_2)$;

Initialize $t=1,n=1$

While $t<mn>5</mn><mn>0</mn><mn>0</mn><mn>0</mn>$ do:

ReceivNum $=0$

While $($:$x_n>x_2$