Paradigms for Optimization Problems

In this chapter, we consider fundamental optimization problems that occur in many real-life applications. The few selected core optimization problems are very representative of a broad class of mathematical problems encountered in practice. A major characteristic of these problems is that they are all combinatorial by essence. This means that the optimization algorithms described in the following are not approaching an optimal solution numerically (by say, a Newton-like gradient descent method as seen previously in Chapter § 2), but rather exploring and searching for exact solutions in large but finite discrete configuration spaces. The optimization techniques presented in the remainder are broad enough that their underlying schemes can be used for solving various problems; these different kinds of solving methodologies are called paradigms since they yield generic algorithms for tackling many similar problems.