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Three modeling paradigms in mathematical programming

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Abstract

Celebrating the sixtieth anniversary since the zeroth International Symposium on Mathematical Programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonlinear programming, and variational inequalities. We will describe the modeling approaches, mathematical formulations, and recent results of these paradigms, and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems. Our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field.

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  1. Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL, 61801, USA

    Jong-Shi Pang

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Correspondence to Jong-Shi Pang.

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The work is based on researach supported by the National Science Foundation under grants CMMI-0802022 and DMS-0754374, the Office of Naval Research under grant no. N00014-06-1-0014, and the Air Force Office of Sponsored Research under grant FA9550-08-1-0061.

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Pang, JS. Three modeling paradigms in mathematical programming. Math. Program. 125, 297–323 (2010). https://doi.org/10.1007/s10107-010-0395-1

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