The Persistence and Effectiveness of Large-Scale Mathematical Programming Strategies: Projection, Outer Linearization, and Inner Linearization
Geoffrion  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.
KeywordsColumn Generation SIAM Journal Interior Point Method Outer Approximation Cutting Plane Algorithm
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- 1.Abhishek K, Leyffer S, Linderoth JT (2008) FilMINT: An outer-approximation-based solver for nonlinear mixed integer programs. Argonne National Laboratory, Mathematics and Computer Science Division Preprint ANL/MCS-P1374-0906, March 28Google Scholar
- 4.Bellman R (1957) Dynamic programming. Princeton University Press, Princeton, NJGoogle Scholar
- 6.Bertsekas DP, Yu H (2009) A unifying polyhedral approximation framework for convex optimization. MIT Working Paper: Report LIDS–2820, SeptemberGoogle Scholar
- 12.Dantzig GB (1963) Linear programming and extensions. Princeton University Press, Princeton, NJGoogle Scholar
- 13.Dantzig GB, Madansky A (1961) On the solution of two–stage linear programs under uncertainty. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, CAGoogle Scholar
- 21.Kelley JE (1960) The cutting plane method for solving convex programs. Journal of SIAM 8:703–712Google Scholar
- 25.Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton, NJGoogle Scholar
- 26.Rosen JB (1963) Convex partition programming. In: Graves RL, Wolfe P (eds) Recent advances in mathematical programming. McGraw-Hill, New York, NYGoogle Scholar