Preliminary

This chapter reviews some preliminary that will be used in later chapters. First, we introduce useful definitions of vectors, sets, and functions. Then, the basics of probability and risk measures are summarized. Subsequently, optimization theories are reviewed, including convex optimization, conic programs and duality, multi-objective optimization, stochastic programming, and robust optimization. Some results are stated without proof and references are given for readers interested in the details. Besides the mathematical preliminary, we also summarize some popular power flow models, which are useful in power system planning and operation.