Abstract
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.
This chapter is dedicated to Arthur M. Geoffrion for his many contributions to operations research, management science, and mathematical programming. The work was supported by The University of Chicago Booth School of Business.
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Birge, J.R. (2010). The Persistence and Effectiveness of Large-Scale Mathematical Programming Strategies: Projection, Outer Linearization, and Inner Linearization. In: Sodhi, M., Tang, C. (eds) A Long View of Research and Practice in Operations Research and Management Science. International Series in Operations Research & Management Science, vol 148. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6810-4_3
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DOI: https://doi.org/10.1007/978-1-4419-6810-4_3
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