Abstract
The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an ε-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the ε-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.
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Loridan, P., Morgan, J. (1989). ε-Regularized two-level optimization problems: Approximation and existence results. In: Dolecki, S. (eds) Optimization. Lecture Notes in Mathematics, vol 1405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083589
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DOI: https://doi.org/10.1007/BFb0083589
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