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An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application

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  • S. Siddiqui
  • S. Gabriel

Abstract

This paper presents a new method for solving mathematical programs with equilibrium constraints. The approach uses a transformation of the original problem via Schur’s decomposition coupled with two separate formulations for modeling related absolute value functions. The first formulation, based on SOS1 variables, when solved to optimality will provide a global solution to the MPEC. The second, penalty-based formulation is used to heuristically obtain local solutions to large-scale MPECs. The advantage of these methods over disjunctive constraints for solving MPECs is that computational time is much lower, which is corroborated by numerical examples. Finally, an application of the method to an MPEC representing the United States natural gas market is given. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • S. Siddiqui & S. Gabriel, 2013. "An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application," Networks and Spatial Economics, Springer, vol. 13(2), pages 205-227, June.
    • Handle: RePEc:kap:netspa:v:13:y:2013:i:2:p:205-227
    DOI: 10.1007/s11067-012-9178-y
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    References listed on IDEAS

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    1. Gabriel, S.A. & Rosendahl, K.E. & Egging, Ruud & Avetisyan, H.G. & Siddiqui, S., 2012. "Cartelization in gas markets: Studying the potential for a “Gas OPEC”," Energy Economics, Elsevier, vol. 34(1), pages 137-152.
    2. Rolf Golombek & Eystein Gjelsvik & Knut Einar Rosendahl, 1995. "Effects of Liberalizing the Natural Gas Markets in Western Europe," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 85-112.
    3. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    4. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    5. S A Gabriel & R García-Bertrand & P Sahakij & A J Conejo, 2006. "A practical approach to approximate bilinear functions in mathematical programming problems by using Schur's decomposition and SOS type 2 variables," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(8), pages 995-1004, August.
    6. Yihsu Chen & Benjamin Hobbs & Sven Leyffer & Todd Munson, 2006. "Leader-Follower Equilibria for Electric Power and NO x Allowances Markets," Computational Management Science, Springer, vol. 3(4), pages 307-330, September.
    7. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.
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