Solutions
Solve the proposed problems about constrained optimization.
Here, we’ll review the solutions to the exercise problems of constrained optimization.
Exercise 1: A simple contained problem
The first problem was:
Here, we have two constraints. The first one is a good constraint. We can use it to reduce the number of variables. Let’s use it to get rid of the variable:
Now we have a univariate problem with a single constraint. This constraint is a bad constraint. But we know a method to solve this kind of problem. As , then . If we look at the graph of the function, we see that it’s bitonic for those values of and that the minimum lies somewhere between and . So we can solve the problem with a ternary search.
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