Problem 1 (Optimization problems you are interested in). Optimization problems are usually posed in the following way: let x be a vector of variables that describe the quantities that are subject to optimization (i.e. the design variables u introduced in the first class) and auxiliary variables (i.e. the state variables y); then the problem is to find that vector x for which f(c) min! g(0) = 0, h() > 0 with an objective function f(x), a function g(x) that describes equalities that need to hold at the solution, and h(x) inequalities. Both g and h can be vector-valued, and in this case the (in)equalities have to hold for each element 91(2), 92.0),...,h1(2), h2(2),.... Pick an optimization problem in an area you find interesting. Describe as best as you can: What are the variables that make up x? 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