Find a minimum of the function fx x33-2x23x1 on an

Question

Part A-

1. To Do

We all have those days when there are a bajillion things to do, and we don't know how we're going to get it all done. Sonner than later we miss the tasks that we needed to do!

So for this assignment, you should create a ToDo list. It should at least be able to do the following things:

• Add an item to the To-Do list
• Delete an item from the To-Do list
• Print the To-Do list
• All the To-Do's should be written to a file so that you can load it later.

2. Find your weight on other Planets

Before we get into assignment question, lets understand the difference between Weight and Mass.

• Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the pull of gravity on an object.
• Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter. Weight is measured on a scale.
• The Mass of an object doesn't change when an object's location changes. Weight, on the otherhand does change with location.

Part B-

1. Find a minimum of the function f(x) = x³/3-2x²+3x+1 on an interval [0, 3.5]

2. Find a minimum of the function f(x, y) = x⁴+y⁴ - x² y + x y² numerically starting at the initial point x=1, y=0 (feel free to reuse the code from the lecture notebook). See how different choices of the initial point might affect the results (report any other point of local minima which the solution can return).

Optimization problem:

F(x)→min(max)

x∗=argmin(max)_XF(x)

Common family of iterative optimization methods is known as "gradient descent":

x^j+1 = x^j-(+)λ_j?F(x^j),

where ∇F(x) denotes a gradient vector of F in the point x, while λ_j are certain real positive numbers picked up with respect to F(x_j+1)<(>)F(x_j).

Optimization example.

Consider several points on the map and look for a such a centroid location that sum of distances from it to the given points is minimal:

∑_i√(x_i-x∗)²+(y_i-y∗)²→min.

Attachment:- Assignment.rar