An optimization problem typically deals with an objective function to be maximized or minimized that can very often be written in a quadratic form. If the objective function can be written as a positive definite quadratic function, it can be minimized.
What if the objective function needs to be maximized and the maximization yields an unbounded objective function? In this case is it possible to study this as an optimization problem, like convex or non-convex optimization? For example, the objective function is the area of a region dependent on several parameters. I want to maximize this area and it turns out that the maximum is infinity.