Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks

Liers F, Martin A, Merkert M, Mertens N, Michaels D (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Journal of Global Optimization Springer Verlag (Germany)

DOI: 10.1007/s10898-020-00974-0

Abstract

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integer nonlinear problems that uses simultaneous convexification. We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations.

Authors with CRIS profile

Frauke Liers-Bergmann Professur für Optimization under Uncertainty & Data Analysis Alexander Martin Economics - Discrete Optimization - Mathematics (EDOM)

Involved external institutions

Otto-von-Guericke-Universität Magdeburg DE Germany (DE) Technische Universität Dortmund DE Germany (DE)

How to cite

APA:

Liers, F., Martin, A., Merkert, M., Mertens, N., & Michaels, D. (2021). Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks. Journal of Global Optimization. https://doi.org/10.1007/s10898-020-00974-0

MLA:

Liers, Frauke, et al. "Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks." Journal of Global Optimization (2021).

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