Basics for Optimization Problem

In this chapter, the basics used in this book for the optimization problem are briefly introduced. The organization is shown as follows: (1) the overview of optimization problems, which gives the general forms and the classifications of optimization problems, and some frequently used models are also illustrated; (2) the introductions for the optimization problems with uncertainties, including the stochastic optimization, robust optimization, and interval optimization; (3) the introductions for the convex optimization, including the semi-definite programming (SDP), second-order cone programming (SOCP), and some convex relaxation skills; (4) the optimization frameworks which are frequently used, including the two-stage optimization, and the bi-level optimization. Six examples and the corresponding case studies based on the classic knapsack problem are reformulated to show different optimization problems. The above models are all important topics and not only used in this book, but also in many engineering scenarios. In summary, the contents in this chapter are some basics for optimization problems. The readers who are interesting in the details can refer to the professional mathematical literature or books listed in the reference and who are familiar with these basic optimization skills can also skip this chapter without any inconvenience.