Homework 6

Problem 6.1 (Network data visualization)

• Use the "Les Miserables Links to an external site." dataset (03_les miserablese_GraphData.txt)
• Visualize the network of (novel) characters as an undirected graph
• Summarize the graph and explain the output
• Calculate the degree and the centrality of this graph
• Find some important nodes (corresponding to key novel characters)
• Will the results change if we assume the graph is directed?

Problem 6.2 (Function Optimization): Optimize any two of the following three functions:

6.2.1. Find the extrema of this variant of the Rosenbrock function Links to an external site., $(100(x^2 -y)^2+(x-1)^2 + 100(z^2-w)^2+(z-1)^2)$, $N=4$, and compare your estimates against the Wolfram Alpha Optimizer Links to an external site..

6.2.2. Find the minimum of the constrained Mishra's Bird function Links to an external site., $f(x,y) = \sin(y) e^{\left [(1-\cos x)^2\right]} + \cos(x) e^{\left [(1-\sin y)^2 \right]} + (x-y)^2$, subject to the constraint $(x+5)^2 + (y+5)^2 < 25$.

6.2.3. Minimize the function $f(x,y,z)=-(x^3+5y-2^z)$
subject to $\begin{cases} x -\frac{y}{2}+z^2 \leq 50\\ \mod(x, 4) + \frac{y}{2} \leq 1.5 \end{cases} .$ Check you solution against the Wolfram Alpha solution. Links to an external site.

As usual, your submission should include two files, the RMD (source) and the HTML (knitted report).