Schweiger, Jonas. <br/><br/>
Exploiting Structure in Non-Convex Quadratic Optimization and Gas Network Planning under Uncertainty. 

 - 1st ed. 
 - 1 online resource (206 pages) 
<br/><br/>Intro -- 1 Introduction -- 2 Concepts -- 2.1 Classes of mathematical programs -- 2.2 Introduction to MINLP -- 2.2.1 LP-based branch-and-bound for MILP -- 2.2.2 Convexification -- 2.2.3 Branch-and-bound for MINLP: Spatial Branching -- 2.3 Robust Optimization -- 2.3.1 Multistage Robust Optimization -- 3 Reformulations and relaxations for quadratic programs -- 3.1 Definitions and notation -- 3.2 Convexification -- 3.2.1 McCormick relaxation -- 3.2.2 Convex relaxations by matrix decomposition -- 3.3 Reformulation-Linearization Technique (RLT) -- 3.3.1 Projected RLT inequalities -- 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 -- 4.5.1 Exact separation -- 4.5.2 Heuristic separations and strengthening -- 4.6 Computational Experiments -- 4.6.1 Instances -- 4.6.2 Optimizing over the bipartite closures -- 4.6.3 Combining the separation of MSC and GMSC bipartite inequalities -- 4.6.4 Motzkin-Straus Clique inequalities for higher clique numbers -- 4.6.5 Branch-and-cut results -- 4.6.6 Computational results on the instances from [ST08] -- 4.7 Generalization -- 4.7.1 Computational experiments -- 4.8 Conclusion -- 5 Strong Relaxations for the Pooling Problem -- 5.1 Introduction -- 5.2 Standard formulations -- 5.2.1 Notation and assumptions -- 5.2.2 The flow model -- 5.2.3 The p-formulation -- 5.2.4 The q-formulation -- 5.2.5 The pq-formulation -- 5.3 New convex relaxations for the pooling problem -- 5.3.1 A 5 variable relaxation -- 5.3.2 Extreme points -- 5.3.3 Valid inequalities -- 5.3.4 Convex hull analysis -- 5.4 Computational experiments -- 5.4.1 Computational setup -- 5.4.2 Adding the inequalities -- 5.4.3 Instances -- 5.4.4 Results. 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 -- 7.4.1 From the solutions of the subproblems -- 7.4.2 1-opt heuristic -- 7.4.3 Best-known heuristic -- 7.5 Reusing solutions -- 7.6 Computational Experiments -- 7.6.1 Computational Setup -- 7.6.2 Testsets and Instances -- 7.6.3 Results -- 7.7 Conclusion -- 8 Conclusion. 
<br/><br/><label>ISBN: </label>9783832590949 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Computer science.
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Electronic books.
<br/><br/><label>LC Class. No.: </label>QA76 .S394 2018 
<br/><br/><label>Dewey Class. No.: </label>4