Mixed Integer Models for the Stationary Case of Gas Network Optimization

Martín, Alexander; Möller, Markus; Moritz, Susanne

doi:10.1007/s10107-005-0665-5

Cited by 202 publications

(167 citation statements)

References 14 publications

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“…Some optimization problems involving non-convex piecewise linear functions can be found in applications such as water networks, heat exchanger networks, and distillation sequences [86] stationary gas network optimization [87], merge-in-transit distribution systems, including the integration of inventory and transportation decisions [88], among others.…”

Section: Piecewise Linear Functions and Non-convex Optimizationmentioning

confidence: 99%

Global optimization of non-convex piecewise linear regression splines

et al. 2017

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Section: Piecewise Linear Functions and Non-convex Optimizationmentioning

confidence: 99%

Global optimization of non-convex piecewise linear regression splines

et al. 2017

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“…(In fact, this was already suggested by Beale [70] and Tomlin [52] in the context of non-convex NLPs.) A recent exploration of this idea was conducted by Martin et al [27]. As well as constructing such PLFs, they also propose adding cutting planes to tighten the relaxation.…”

Section: Conversion To An Milpmentioning

confidence: 99%

Non-convex mixed-integer nonlinear programming: A survey

Burer

Letchford

2012

Surveys in Operations Research and Management Science

380

238

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“…and because the objective function tangents represented by (49) and (51) that utilize piecewise linear approximations (e.g., see Martin et al 2006, where the focus is on nonseparable functions). Moreover, by suitably increasing the number of segments, T , in the MIP approximation, along with the number of tangential supports, t + 1 , for the objective function to obtain sufficient granularity, we can accordingly derive a desired near-optimal solution to problem NETO.…”

Section: Algorithm A3: Mixed-integer Programmingmentioning

confidence: 99%

The Nested Event Tree Model with Application to Combating Terrorism

Lunday

Sherali

Glickman

2010

INFORMS Journal on Computing

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I n this paper, we model and solve the strategic problem of minimizing the expected loss inflicted by a hostile terrorist organization. An appropriate allocation of certain capability-related, intent-related, vulnerabilityrelated, and consequence-related resources is used to reduce the probabilities of success in the respective attackrelated actions and to ameliorate losses in case of a successful attack. We adopt a nested event tree optimization framework and formulate the problem as a specially structured nonconvex factorable program. We develop two branch-and-bound schemes based, respectively, on utilizing a convex nonlinear relaxation and a linear outer approximation, both of which are proven to converge to a global optimal solution. We also design an alternative direct mixed-integer programming model representation for this case, and we investigate a fundamental special-case variant for this scheme that provides a relaxation and affords an optimality gap measure. Several range reduction, partitioning, and branching strategies are proposed, and extensive computational results are presented to study the efficacy of different compositions of these algorithmic ingredients, including comparisons with the commercial software BARON. A sensitivity analysis is also conducted to explore the effect of certain key model parameters.

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Mixed Integer Models for the Stationary Case of Gas Network Optimization

Cited by 202 publications

References 14 publications

Global optimization of non-convex piecewise linear regression splines

Global optimization of non-convex piecewise linear regression splines

Non-convex mixed-integer nonlinear programming: A survey

The Nested Event Tree Model with Application to Combating Terrorism

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