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Complementarity-Based Nonlinear Programming Techniques for Optimal Mixing in Gas Networks

Falk M. Hante(hante***at***math.fau.de)
Martin Schmidt(mar.schmidt***at***fau.de)

Abstract: We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems and show that mixed-integer reformulations of pooling-type mixing models already render small-size instances intractable. Therefore we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we show that classical stationarity concepts are meaningful for the resulting complementarity-based reformulation of the mixing equations. We test this approach numerically by comparing such a reformulation with a more compact complementarity-based one that does not feature such beneficial regularity properties. All computations are performed on publicly available data of real-world size problem instances from steady-state gas transport. Our numerical results show that both complementarity-based models outperform the mixed-integer reformulation significantly and that the complementarity-based model with beneficial regularity properties can be solved more reliable.

Keywords: Gas transport networks, Mixing, Inverse parametric quadratic programming, Complementarity constraints, MPCC

Category 1: Nonlinear Optimization

Category 2: Applications -- Science and Engineering

Category 3: Complementarity and Variational Inequalities

Citation:

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Entry Submitted: 09/12/2017
Entry Accepted: 09/12/2017
Entry Last Modified: 09/12/2017

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