Variational Inequality Problems

Steven A. Gabriel, Antonio J. Conejo, J. David Fuller, Benjamin F. Hobbs and Carlos Ruiz
Additional contact information
Steven A. Gabriel: University of Maryland
Antonio J. Conejo: University of Castilla – La Mancha
J. David Fuller: University of Waterloo
Benjamin F. Hobbs: The Johns Hopkins University
Carlos Ruiz: European Foundation for New Energy – EDF École Centrale Paris and Supélec

Chapter Chapter 5 in Complementarity Modeling in Energy Markets, 2013, pp 181-220 from Springer

Abstract: Abstract The purpose of this chapter is to explain variational inequality (VI) formulations of equilibrium problems, and the close connection of a VI problem to an equivalent complementarity problem. There are sometimes advantages to a VI formulation compared to a complementarity formulation: the complementarity formulation has primal decision variables, and dual variables that arise, e.g., when specifying the KKT conditions of individual agents; but a VI formulation has the same primal variables, with few, or no dual variables, which can considerably ease the coding of the model in GAMS. This coding advantage is particularly evident when implementing large complex models, or decomposition algorithms as discussed in Chapter 9. However, the derivation of a complementarity model formulation is usually easier than the derivation of an equivalent VI model: e.g., many complementarity models in this book are derived by writing down the KKT conditions of the agents, together with market-clearing conditions, but the procedure to write down a VI model with few or no dual variables is not as easily stated. In this chapter, we alleviate this difficulty by showing how to arrive quickly at the formulation of a VI model for a large class of Nash equilibrium and generalized Nash equilibrium settings.

Keywords: Nash Equilibrium; Variational Inequality; Complementarity Problem; Dual Variable; Variational Inequality Problem (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4419-6123-5_5

Ordering information: This item can be ordered from
http://www.springer.com/9781441961235

DOI: 10.1007/978-1-4419-6123-5_5

Access Statistics for this chapter

More chapters in International Series in Operations Research & Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().