A party optimization example

In this example, imagine that you are throwing a party and inviting five friends. We will give them unique names from Alice to Frank, as shown in Figure 5.8. You have made an estimate of how much each of your friends contributes to the energy of a party. These are the linear or diagonal terms in the table in Figure 5.8. Your values are from -1 (a negative contribution to the party) to +1 (a maximum positive contribution to the party). For example, Alice has the most positive contribution to a party of 0.5, while Eve who does not contribute to the energy at parties has a value of -1.

Now, you also realize that not only do each of your friends individually contribute to a party’s energy but their energy contribution changes, depending on who else is at the party with them. You are feeling quite sophisticated for having determined that pair-wise relationships or quadratic relationships are important in this case. You recall how each pair of friends...