Solving Mixed-Integer Programming Problems Using Piecewise Linearization Methods

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2017
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Zusammenfassung

We present an overview on piecewise linearization methods for MINLPs. This will include the concept of disjunctive constraints, which is necessary to define logarith- mic reformulations of the so called disaggregated convex combination method and the convex combination method. For the case of a general univariate quadratic func- tion we also calculate the linearization error and proof that equidistant grid points minimize this error. For a bivariate product of two variables we do the same error analysis for the case of J 1 -triangulations and again equidistant grid points will be optimal. The presented methods will then be applied to a newly developed model for a hybrid energy supply network problem. We show that linearizations are able to solve this non-convex optimization problem within reasonable time.

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Fachgebiet (DDC)
510 Mathematik
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Mixed-integer optimization, nonlinear programming, piecewise linearization, branch-and-bound methods
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ISO 690BERNREUTHER, Marco, 2017. Solving Mixed-Integer Programming Problems Using Piecewise Linearization Methods [Bachelor thesis]. Konstanz: Universität Konstanz
BibTex
@mastersthesis{Bernreuther2017Solvi-40493,
  year={2017},
  title={Solving Mixed-Integer Programming Problems Using Piecewise Linearization Methods},
  address={Konstanz},
  school={Universität Konstanz},
  author={Bernreuther, Marco}
}
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Konstanz, Universität Konstanz, Bachelorarbeit, 2017
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