Abstract
Many optimization problems in practice have continuous and discrete variables. Formally, one can plug the discrete variables in the superset (called \(\hat {S}\)) of the constraint set, but then this set is nonconvex and the Lagrange multiplier rule in Chap. 5 is not applicable and the duality theory in Chap. 6 is only limitedly applicable. For a Lagrange theory and a duality theory in discrete-continuous nonlinear optimization one needs a different approach, which is developed in this chapter. The main key for such a theory is a special separation theorem for discrete sets. Using this theory we present optimality conditions as well as duality results.
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Notes
- 1.
J. Jahn and M. Knossalla, “Lagrange theory of discrete-continuous nonlinear optimization”, Journal of Nonlinear and Variational Analysis 2 (2018) 317–342.
References
C. Geiger and C. Kanzow, Theorie und Numerik restringierter Optimierungsaufgaben (Springer, 2002).
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Jahn, J. (2020). Extension to Discrete-Continuous Problems. In: Introduction to the Theory of Nonlinear Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-42760-3_8
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DOI: https://doi.org/10.1007/978-3-030-42760-3_8
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