Moritz Link

University of Konstanz | Uni-Konstanz · Department of Mathematics and Statistics

In this work, we present an algorithm for computing an enclosure for multi-objective mixed-integer nonconvex optimization problems. In contrast to existing solvers for this type of problem, this algorithm is not based on a branch-and-bound scheme but rather relies on a relax-and-refine approach. While this is an established technique in single-obje...

A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, th...

In this paper, a new method for computing an enclosure of the nondominated set of multiobjec- tive mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method cho...

In this report, a detailed description of an MINLP model for decentralized energy supply network optimization is given. This model includes the possibility of extending gas transmission lines, local choice of heating technology, as well as local decisions for energy-efficient house renovation. Ultimately, the model is aimed at finding cost-efficien...

In this paper, a new method for computing an enclosure of the nondom-inated set of multiobjective mixed-integer problems without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level...

Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any Henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show th...

Given a henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show th...