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Optimality conditions in discrete-continuous nonlinear optimization

Gabriele Eichfelder(gabriele.eichfelder***at***tu-ilmenau.de)
Johannes Jahn(johannes.jahn***at***fau.de)

Abstract: This paper presents 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.

Keywords: nonlinear optimization; optimality conditions; discrete-continuous variables; mixed-integer nonlinear problems

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 06/19/2020
Entry Accepted: 06/19/2020
Entry Last Modified: 06/19/2020

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