Approximating Security Values of MinSup Problems with Quasi-variational Inequality Constraints
We consider a two-stage model where a leader, according to its risk-averse proneness, solves a MinSup problem with constraints corresponding to the reaction sets of a follower and defined by the solutions of a quasi-variational inequality (i.e. a variational inequality having constraint sets depending on its own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. In general the infimal value of a MinSup (or the maximal value of a MaxInf) problem with quasi-variational inequality constraints is not stable under perturbations in the sense that the sequence of optimal values for the perturbed problems may not converge to the optimal value of the original problem even in presence of nice data. Thus, we introduce different types of approximate values for this problem, we investigate their asymptotical behavior under perturbations and we emphasized the results concerning MinSup problems with variational inequality constraints as well results holding under stronger assumptions that can be more easily employed in applications.
|Date of creation:||14 Sep 2012|
|Date of revision:||09 Oct 2014|
|Publication status:||Published in Pacific Journal of Optimization, 2014, 10(4), pp. 749-765|
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- Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, 01.
- M. Lignola & Jacqueline Morgan, 2012. "Approximate values for mathematical programs with variational inequality constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 485-503, October.
- Laurent Drouet & Alain Haurie & Francesco Moresino & Jean-Philippe Vial & Marc Vielle & Laurent Viguier, 2008. "An oracle based method to compute a coupled equilibrium in a model of international climate policy," Computational Management Science, Springer, vol. 5(1), pages 119-140, February.
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