We introduce in this chapter the notation used throughout the book (see also the list of symbols), as well as the necessary mathematical background to make the book self-contained. Section 1.2 gives useful results from combinatorics, some of them being quite standard while some others are specific, and most often proofs are provided. The rest of the chapter (Sect. 1.3) gives condensed summaries about binary relations, partially ordered sets, inequalities and polyhedra, linear programming, convexity, convex optimization, etc. Of course, no proof is provided there and readers who are unfamiliar with these topics and finding the exposition rather dry should consult the mentioned references.
KeywordsPartial Order Binary Relation Distributive Lattice Duality Theorem Nonempty Closed Convex Subset
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