Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty
Jonas Schweiger
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Jonas Schweiger, Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty (2018), Logos Verlag, Berlin, ISBN: 9783832590949
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Beschreibung / Abstract
The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, Jonas Schweiger addresses applications, where nonconvexity in the model and uncertainty in the data pose principal difficulties. In the first part, he contributes strong relaxations for non-convex problems such as the non-convex quadratic programming and the Pooling Problem. In the second part, he contributes a robust model for gas transport network extension and a custom decomposition approach. All results are backed by extensive computational studies.
Beschreibung
Jonas Schweiger pursued his doctoral studies while having positions at Zuse Institute Berlin and IBM CPLEX Optimization and a scholarship by the CRC TRR 154. His research focuses on the application of mathematical optimization and non-convex MINLP. In 2017 he finished his PhD and returned to Zuse Institute Berlin where he is currently leading the research group Energy Network Optimization.
Inhaltsverzeichnis
- BEGINN
- 1 Introduction
- 2 Concepts
- 2.1 Classes of mathematical programs
- 2.2 Introduction to MINLP
- 2.3 Robust Optimization
- 3 Reformulations and relaxations for quadratic programs
- 3.1 Definitions and notation
- 3.2 Convexification
- 3.3 Reformulation-Linearization Technique (RLT)
- 4 Motzkin-Straus inequalities for Standard Quadratic Programming and generalizations
- 4.1 Introduction
- 4.2 Q-Space reformulation for StQP
- 4.3 Motzkin-Straus Clique inequalities
- 4.4 Generalized MSC inequalities for bipartite graphs
- 4.5 Separation
- 4.6 Computational Experiments
- 4.7 Generalization
- 4.8 Conclusion
- 5 Strong Relaxations for the Pooling Problem
- 5.1 Introduction
- 5.2 Standard formulations
- 5.3 New convex relaxations for the pooling problem
- 5.4 Computational experiments
- 5.5 Conclusion
- 6 Models for deterministic gas network optimization
- 6.1 Introduction
- 6.2 Modeling gas transportation networks
- 6.3 Deterministic network extension
- 7 Gas network topology planning for multiple scenarios
- 7.1 A robust model for gas network extension
- 7.2 Scenario decomposition: A branch-and-bound approach
- 7.3 Dual bounds
- 7.4 Primal solutions
- 7.5 Reusing solutions
- 7.6 Computational Experiments
- 7.7 Conclusion
- 8 Conclusion