# Minimize the function h(x,y) = x^2*(1+sin(y/3)*cos(8*x)) + y^2*(2 + cos(5*x)*cos(8*y)) for x, y…

```Minimize the function h(x,y) = x^2*(1+sin(y/3)*cos(8*x)) + y^2*(2 + cos(5*x)*cos(8*y)) for x, y between (-2,2) using
# stochastic gradient descent (SGD) methods.
# 1) Make a 3D plot
# 2) Make an "hotmap" image with contour plots
# 3) Add starting/ending points to the hotmap along with lines from SGD.
# 4) Show the "optimal" objective value from SGD and corresponding (x,y) values.
# 5) Using your SGD to maximize this function: h = function(x){(cos(50*x)+sin(20*x))^2}. Note: you may need to fine tune your parameters (alpha/beta). Comment on the results.```

```%%R
set.seed(2021)

# note the "-" for maximumization
h = function (x,y) {
-x^2*(1+sin(y/3)*cos(8*x)) - y^2*(2 + cos(5*x)*cos(8*y))
}
h2 =function(x){
-x^2*(1+sin(x/3)*cos(8*x)) - x^2*(2 + cos(5*x)*cos(8*x))
}```

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