Efstratios N. Pistikopoulos, Nikolaos A. Diangelakis, Richard Oberdieck

Multi-Parametric Optimization and Control

• Gebundenes Buch

Produktbeschreibung

Recent developments in multi-parametric optimization and control

Multi-Parametric Optimization and Control provides comprehensive coverage of recent methodological developments for optimal model-based control through parametric optimization. It also shares real-world research applications to support deeper understanding of the material.

Researchers and practitioners can use the book as reference. It is also suitable as a primary or a supplementary textbook. Each chapter looks at the theories related to a topic along with a relevant case study. Topic complexity increases gradually as readers progress through the chapters. The first part of the book presents an overview of the state-of-the-art multi-parametric optimization theory and algorithms in multi-parametric programming. The second examines the connection between multi-parametric programming and model-predictive control--from the linear quadratic regulator over hybrid systems to periodic systems and robust control.

The third part of the book addresses multi-parametric optimization in process systems engineering. A step-by-step procedure is introduced for embedding the programming within the system engineering, which leads the reader into the topic of the PAROC framework and software platform. PAROC is an integrated framework and platform for the optimization and advanced model-based control of process systems.
_ Uses case studies to illustrate real-world applications for a better understanding of the concepts presented
_ Covers the fundamentals of optimization and model predictive control
_ Provides information on key topics, such as the basic sensitivity theorem, linear programming, quadratic programming, mixed-integer linear programming, optimal control of continuous systems, and multi-parametric optimal control

An appendix summarizes the history of multi-parametric optimization algorithms. It also covers the use of the parametric optimization toolbox (POP), which is comprehensive software for efficiently solving multi-parametric programming problems.

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Produktdetails

• Wiley Series in Operations Research and Management Science
• Verlag: Wiley / Wiley & Sons
• Artikelnr. des Verlages: 1W119265180
• 1. Auflage
• Seitenzahl: 320
• Erscheinungstermin: 24. November 2020
• Englisch
• Abmessung: 224mm x 148mm x 20mm
• Gewicht: 326g
• ISBN-13: 9781119265184
• ISBN-10: 1119265185
• Artikelnr.: 58020868

Autorenporträt

EFSTRATIOS N. PISTIKOPOULOS is the Director of the Texas A&M Energy Institute and a TEES Eminent Professor in the Artie McFerrin Department of Chemical Engineering at Texas A&M University. He holds a Ph.D. degree from Carnegie Mellon University (1988) and was with Shell Chemicals in Amsterdam before joining Imperial. He has authored or co-authored over 500 major research publications in the areas of modelling, control and optimization of process, energy and systems engineering applications, 15 books and 2 patents. NIKOLAOS A. DIANGELAKIS is an Optimization Specialist at Octeract Ltd. He holds a PhD and MSc on Advanced Chemical Engineering from Imperial College London and was a member of the Multi-Parametric Optimization and Control group at Imperial and then Texas A&M since 2011. He is the co-author of 16 journal papers, 11 conference papers and 3 book chapters. RICHARD OBERDIECK is a Technical Account Manager at Gurobi Optimization, LLC. He obtained a bachelor and MSc degrees from ETH Zurich in Switzerland (2009-1013), before pursuing a PhD in Chemical Engineering at Imperial College London, UK, which he completed in 2017. He has published 21 papers and 2 book chapters, has an h-index of 11 and was awarded the FICO Decisions Award 2019 in Optimization, Machine Learning and AI.

Inhaltsangabe

Short Bios of the Authors xvii

Preface xxi

1 Introduction 1

1.1 Concepts of Optimization 1

1.1.1 Convex Analysis 1

1.1.1.1 Properties of Convex Sets 2

1.1.1.2 Properties of Convex Functions 2

1.1.2 Optimality Conditions 3

1.1.2.1 Karush-Kuhn-Tucker Necessary Optimality Conditions 5

1.1.2.2 Karun-Kush-Tucker First-Order Sufficient Optimality Conditions 5

1.1.3 Interpretation of Lagrange Multipliers 6

1.2 Concepts of Multi-parametric Programming 6

1.2.1 Basic Sensitivity Theorem 6

1.3 Polytopes 9

1.3.1 Approaches for the Removal of Redundant Constraints 11

1.3.1.1 Lower-Upper Bound Classification 12

1.3.1.2 Solution of Linear Programming Problem 13

1.3.2 Projections 13

1.3.3 Modeling of the Union of Polytopes 14

1.4 Organization of the Book 16

References 16

Part I Multi-parametric Optimization 19

2 Multi-parametric Linear Programming 21

2.1 Solution Properties 22

2.1.1 Local Properties 23

2.1.2 Global Properties 25

2.2 Degeneracy 28

2.2.1 Primal Degeneracy 29

2.2.2 Dual Degeneracy 30

2.2.3 Connections Between Degeneracy and Optimality Conditions 31

2.3 Critical Region Definition 32

2.4 An Example: Chicago to Topeka 33

2.4.1 The Deterministic Solution 34

2.4.2 Considering Demand Uncertainty 35

2.4.3 Interpretation of the Results 36

2.5 Literature Review 38

References 39

3 Multi-Parametric Quadratic Programming 45

3.1 Calculation of the Parametric Solution 47

3.1.1 Solution via the Basic Sensitivity Theorem 47

3.1.2 Solution via the Parametric Solution of the KKT Conditions 48

3.2 Solution Properties 49

3.2.1 Local Properties 49

3.2.2 Global Properties 50

3.2.3 Structural Analysis of the Parametric Solution 52

3.3 Chicago to Topeka with Quadratic Distance Cost 55

3.3.1 Interpretation of the Results 56

3.4 Literature Review 61

References 63

4 Solution Strategies for mp-LP and mp-QP Problems 67

4.1 General Overview 68

4.2 The Geometrical Approach 70

4.2.1 Define A Starting Point Theta0 70

4.2.2 Fix Theta0 in Problem (4.1), and Solve the Resulting QP 71

4.2.3 Identify The Active Set for The Solution of The QP Problem 72

4.2.4 Move Outside the Found Critical Region and Explore the Parameter Space 72

4.3 The Combinatorial Approach 75

4.3.1 Pruning Criterion 76

4.4 The Connected-Graph Approach 78

4.5 Discussion 81

4.6 Literature Review 83

References 85

5 Multi-parametric Mixed-integer Linear Programming 89

5.1 Solution Properties 90

5.1.1 From mp-LP to mp-MILP Problems 90

5.1.2 The Properties 91

5.2 Comparing the Solutions from Different mp-LP Problems 92

5.2.1 Identification of Overlapping Critical Regions 93

5.2.2 Performing the Comparison 95

5.2.3 Constraint Reversal for Coverage of Parameter Space 95

5.3 Multi-parametric Integer Linear Programming 96

5.4 Chicago to Topeka Featuring a Purchase Decision 99

5.4.1 Interpretation of the Results 99

5.5 Literature Review 102

References 103

6 Multi-parametric Mixed-integer Quadratic Programming 107

6.1 Solution Properties 109

6.1.1 From mp-QP to mp-MIQP Problems 109

6.1.2 The Properties 109
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