303
2020
eng
36
preprint
0
2020-02-12
2020-02-12
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Solving Mixed-Integer Nonlinear Optimization Problems using Simultaneous Convexification - a Case Study for Gas Networks
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.
2
Creative Commons - CC BY-NC - Namensnennung - Nicht kommerziell 4.0 International
Frauke Liers
Alexander Martin
Maximilian Merkert
Nick Mertens
Dennis Michaels
eng
uncontrolled
Mixed-Integer Nonlinear Programming
eng
uncontrolled
Simultaneous Convexification
eng
uncontrolled
Convex Envelope
eng
uncontrolled
Gas Network Optimization
Friedrich-Alexander-Universität Erlangen-Nürnberg
A05
B06
B07
Z01
https://opus4.kobv.de/opus4-trr154/files/303/SolMINLPsusingSimConv.pdf