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Optimality Conditions in Discrete-Continuous Nonlinear Optimization
Minimax theory and its applications, Tome 6 (2021) no. 1
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We present necessary and sufficient optimality conditions for discrete-continuous nonlinear optimization problems including mixed-integer nonlinear problems. This theory does not utilize an extension of the Lagrange theory of continuous optimization but it works with certain max functionals for a separation of two sets where one of them is nonconvex. These functionals have the advantage that they can be used for nonconvex optimization problems. This theory avoids getting several Lagrange multipliers per constraint.
Mots-clés : Nonlinear optimization, optimality conditions, discrete-continuous variables, mixedinteger nonlinear problems 
@article{MTA_2021_6_1_a3,
     author = {Gabriele Eichfelder,Johannes Jahn},
     title = {Optimality {Conditions} in {Discrete-Continuous} {Nonlinear} {Optimization}},
     journal = {Minimax theory and its applications},
     year = {2021},
     volume = {6},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2021_6_1_a3/}
}
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Gabriele Eichfelder,Johannes Jahn. Optimality Conditions in Discrete-Continuous Nonlinear Optimization. Minimax theory and its applications, Tome 6 (2021) no. 1. http://geodesic.mathdoc.fr/item/MTA_2021_6_1_a3/