A new approach to the two-level problem
Keywords:
Two-level problems, Equilibrium problems, Pareto minimumsAbstract
Our interest is to formulate the two-level problem as an optimization problem on weak efficient sets, because in this way we can apply all the theory developed for weak efficient sets to two-level problems. The connection between both problems is the equilibrium problem.
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Blum, E., and Oettli, W., From Optimization and Variational Inequalities to Equilibrium Problems, The Mathematics Student, 63 (1994) 123-145
A.N. Iusem, W. Sosa, New existence results for equilibrium problems, Nonlinear Analysis 52 (2003) 621-635.
A. N. Iusem, G. Kassay and W. Sosa, On certain conditions for the existence of solutions of solutions of equilibrium problems, To appears in Mathematical Programming.
Raupp, F. M. P., and Sosa, W., An analytic center cutting plane algorithm for finding equilibrium points. To appears in RAIRO.
W. Sosa and Fernanda M. P. Raupp. A new approach to multicriteria optimization problems, Numerical Algorithms, 35 (2004) 233-247.
J. E. Martinez Legaz and W. Sosa, Duality for Equilibrium Problems, To appears in Journal of Global Optimization.
Rauup, F. M. P., and Sosa, W., Optimzation over weak efficient sets, To appears in Optimization.
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