Problem 2 (Optimization problems you are interested in). Optimization problems are usually posed in the following way: let z be a vector of variables that describe the quantities that are subject to optimization. Some of the components of this vector are design variables (we used the symbol u for these when this scheme was introduced in the first class) and these are the things you can control, i.e., for which you can choose values. The remainder of the variables in the vector I are auxiliary variables (i.e., the state 1 variables y that result from a specific choice of u; you can think if u as the causes and of y as the effects). Then the problem is to find that vector x for which f(:) min! 9(2) = 0, h(x) > 0, with an objective function f(x), a function (2) that describes equalities that need to hold at the solution, and h(2) inequalities. Both g and h can be vector-valued, and in this case the inequalities have to hold for each element 91 (2),g2(2),..., h(), h2(2),..... We all have areas of engineering and the sciences that we find interesting and have spent more time reading about than was maybe strictly necessary for our studies. Pick an optimization problem in an area you find exciting. Describe in as much detail as you can: What are the variables that make up x? Which of these are the controls u and which are the auxiliary variables y? What are the functions f, g, h (i.e. what do they mean) and, if possible, their form as a formula? What can you say about the classification of the problem? In other words, according to the criteria discussed in class, is it convexonconvex, smoothonsmooth, etc.? (The important part isn't whether you get this characterization right, but whether you can justify your characterization.) (30 points)