Abstract
This book is mostly about linear programming. However, this subject, important as it is, is just a subset of a larger subject called convex analysis. In this chapter, we shall give a brief introduction to this broader subject. In particular, we shall prove a few of the fundamental results of convex analysis and see that their proofs depend on some of the theory of linear programming that we have already developed.
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Notes
- 1.
Until now we’ve used subscripts for the components of a vector. In this chapter, subscripts will be used to list sequences of vectors. Hopefully, this will cause no confusion.
- 2.
Given any vector ξ, we use the notation ξ > 0 to indicate that every component of ξ is strictly positive: ξ j  > 0 for all j.
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Vanderbei, R.J. (2014). Convex Analysis. In: Linear Programming. International Series in Operations Research & Management Science, vol 196. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-7630-6_10
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DOI: https://doi.org/10.1007/978-1-4614-7630-6_10
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