Abstract
We study parametric convex lexicographic optimization problems with two objectives. Using basic tools of convex analysis and point-to-set topology, we find conditions for continuity of the optimal value function, give characterizations of global and local optima, and formulate a Lagrangian duality theory. These results are readily applicable to bilevel convex programs
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Floudas, C.A., Zlobec, S. (1998). Optimality and Duality in Parametric Convex Lexicographic Programming. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) Multilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0307-7_16
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DOI: https://doi.org/10.1007/978-1-4613-0307-7_16
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