Networks and Spatial Economics

, Volume 19, Issue 4, pp 1199–1214 | Cite as

A Bicriteria Perspective on L-Penalty Approaches – a Corrigendum to Siddiqui and Gabriel’s L-Penalty Approach for Solving MPECs

  • Kerstin DächertEmail author
  • Sauleh Siddiqui
  • Javier Saez-Gallego
  • Steven A. Gabriel
  • Juan Miguel Morales


This paper presents a corrigendum to Theorems 2 and 3 in Siddiqui and Gabriel (Netw Spatial Econ 13(2):205–227, 2013). In brief, we revise the claim that their L-penalty approach yields a solution satisfying complementarity for any positive value of L, in general. This becomes evident when interpreting the L-penalty method as a weighted-sum scalarization of a bicriteria optimization problem. We also elaborate further assumptions under which the L-penalty approach yields a solution satisfying complementarity.


Equilibrium problems MPEC L-penalty method Bicriteria optimization 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Financial MathematicsFraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany
  2. 2.Departments of Civil Engineering and Applied Mathematics & StatisiticsJohns Hopkins UniversityBaltimoreUSA
  3. 3.Siemens Wind Power A/SBallerupDenmark
  4. 4.Department of Mechanical Engineering, Applied Mathematics, Statistics, and Scientific Computation ProgramUniversity of MarylandCollege ParkUSA
  5. 5.Department of Applied Mathematics, School of Industrial EngineersUniversity of MálagaMálagaSpain

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