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MinSup Problems with Quasi-equilibrium Constraints and Viscosity Solutions

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MinSup problems with constraints described by quasi-equilibrium problems are considered in Banach spaces. The solutions set of such problems may be empty even in very good situations, so the aim of this paper is twofold. First, we determine appropriate regularizations which allow to asymptotically reach the value of the original problem. Then, among these regularizations we identify those which allow to bypass the lack of exact solutions to these problems by a suitable concept of viscosity solution whose existence is then proved under reasonable assumptions.

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  • M. Beatrice Lignola & Jacqueline Morgan, 2015. "MinSup Problems with Quasi-equilibrium Constraints and Viscosity Solutions," CSEF Working Papers 393, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    • Handle: RePEc:sef:csefwp:393
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    1. M. Beatrice Lignola & Jacqueline Morgan, 2014. "Viscosity Solutions for Bilevel Problems with Nash Equilibrium Constraints," CSEF Working Papers 367, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 02 Oct 2014.
    2. 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.
    3. Jacqueline Morgan & Roberto Raucci, 2003. "Lower semicontinuity for approximate social Nash equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 499-509, September.
    4. M. Beatrice Lignola & Jacqueline Morgan, 2012. "Approximating Security Values of MinSup Problems with Quasi-variational Inequality Constraints," CSEF Working Papers 321, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 09 Oct 2014.
    5. L. C. Ceng & N. Hadjisavvas & S. Schaible & J. C. Yao, 2008. "Well-Posedness for Mixed Quasivariational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 109-125, October.
    6. M. B. Lignola & J. Morgan, 2007. "On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 117-121, April.
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