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Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques

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Abstract

We describe a new possibility to model disjunctive optimization problems as generalized semi-infinite programs. In contrast to existing methods in disjunctive programming, our approach does not expect any special formulation of the underlying logical expression. Applying existing lower-level reformulations for the corresponding semi-infinite program, we derive conjunctive nonlinear problems without any logical expressions, which can be locally solved by standard nonlinear solvers. Our preliminary numerical results on some small-scale examples indicate that our reformulation procedure is a reasonable method to solve disjunctive optimization problems.

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Acknowledgments

We thank the anonymous referees, the associate editor and the editor-in-chief for their precise and substantial remarks, which helped to significantly improve the paper. This research was partially supported by the DFG (Deutsche Forschungsgemeinschaft) under Grant STE 772/14-1.

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  1. Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Peter Kirst & Oliver Stein

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  1. Peter Kirst
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  2. Oliver Stein
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Correspondence to Oliver Stein.

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Kirst, P., Stein, O. Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques. J Optim Theory Appl 169, 1079–1109 (2016). https://doi.org/10.1007/s10957-016-0862-9

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  • DOI: https://doi.org/10.1007/s10957-016-0862-9

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