Solving Mixed-Integer Programming Problems Using Piecewise Linearization Methods
2017, Bernreuther, Marco
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.