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Recent developments and future directions in mathematical programming

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2 Author(s)
Johnson, E.L. ; IBM Research Division, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598-0218, USA ; Nemhauser, G.L.

Recent advances in mathematical programming methodology have included: development of interior methods competing with the simplex method, improved simplex codes, vastly improved performance for mixed-integer programming using strong linear programming formulations, and a renewed interest in decomposition. In addition, use of vector and parallel processing has improved performance and influenced algorithmic developments. Application areas have been expanding from the traditional refinery planning and distribution models to include finance, scheduling, manufacturing, manpower planning, and many others. We see the acceleration of better methods and improved codes moving together with faster, lower-cost, and more interesting hardware into a variety of application areas, thereby opening up new demands for greater function of optimization codes. These new functions might include, for example, more powerful nonlinear codes, decomposition techniques taking advantage of network and other problem-dependent structures, and mixed-integer capability in quadratic and general nonlinear problems.Stochastic scenario programming and multitime-period problems are becoming solvable and open up applications and algorithmic challenges. The IBM Optimization Subroutine Library has helped to accelerate these changes but will have to continue to change and expand in ways that are touched upon in this paper.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Systems Journal  (Volume:31 ,  Issue: 1 )