The Persistence and Effectiveness of Large-Scale Mathematical Programming Strategies: Projection, Outer Linearization, and Inner Linearization

  • John R. Birge
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 148)


Geoffrion [19] gave a framework for efficient solution of large-scale mathematical programming problems based on three principal approaches that he described as problem manipulations: projection, outer linearization, and inner linearization. These fundamental methods persist in optimization methodology and underlie many of the innovations and advances since Geoffrion’s articulation of their fundamental nature. This chapter reviews the basic principles in these approaches to optimization, their expression in a variety of methods, and the range of their applicability.


Column Generation SIAM Journal Interior Point Method Outer Approximation Cutting Plane Algorithm 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • John R. Birge
    • 1
  1. 1.Booth School of BusinessUniversity of ChicagoChicagoUSA

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