TY - INPR A1 - Burlacu, Robert A1 - Geißler, Björn A1 - Schewe, Lars T1 - Solving Mixed-Integer Nonlinear Programs using Adaptively Refined Mixed-Integer Linear Programs N2 - We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope an iterative algorithm which solves MIP relaxations that are adaptively refined. We are able to give convergence results for a wide range of MINLPs requiring only continuous nonlinearities with bounded domains and an oracle computing maxima of the nonlinearities on their domain. Moreover, the practicalness of our approach is shown numerically by an application from the field of gas network optimization. KW - Mixed-Integer Nonlinear Programming KW - Piecewise Linearization Y1 - 2017 ER - TY - JOUR A1 - Geißler, Björn A1 - Morsi, Antonio A1 - Schewe, Lars A1 - Schmidt, Martin T1 - Penalty Alternating Direction Methods for Mixed-Integer Optimization: A New View on Feasibility Pumps JF - SIAM Journal on Optimization N2 - Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only few works considering their theoretical properties. We show that feasibility pumps can be seen as alternating direction methods applied to special reformulations of the original problem, inheriting the convergence theory of these methods. Moreover, we propose a novel penalty framework that encompasses this alternating direction method, which allows us to refrain from random perturbations that are applied in standard versions of feasibility pumps in case of failure. We present a convergence theory for the new penalty based alternating direction method and compare the new variant of the feasibility pump with existing versions in an extensive numerical study for mixed-integer linear and nonlinear problems. Y1 - 2017 U6 - https://doi.org/10.1137/16M1069687 VL - 27 IS - 3 SP - 1611 EP - 1636 ER - TY - JOUR A1 - Sirvent, Mathias A1 - Kanelakis, Nikolaos A1 - Geißler, Björn A1 - Biskas, Pandelis T1 - A Linearized Model for the Optimization of the Coupled Electricity and Natural Gas System JF - Journal of Modern Power Systems and Clean Energy N2 - In the following paper a combined optimization of a coupled electricity and gas system is presented. For the electricity network a unit commitment problem with optimization of energy and reserves under a power pool, considering all system operational and unit technical constraints is solved. The gas network subproblem is a medium-scale mixed-integer nonconvex and nonlinear programming problem. The coupling constraints between the two networks are nonlinear as well. The resulting mixed-integer nonlinear program is linearized with the extended incremental method and an outer approximation technique. The resulting model is evaluated using the Greek power and gas system comprising fourteen gas-fired units under four different approximation accuracy levels. The results indicate the efficiency of the proposed MIP model and the interplay between computational requirements and accuracy. KW - Electricity System KW - Natural Gas System KW - Mixed-Integer (Non)Linear Programming KW - Extended Incremental Method KW - Outer Approximation Y1 - 2017 U6 - https://doi.org/10.1007/s40565-017-0275-2 VL - 5 IS - 3 SP - 364 EP - 374 ER -