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Summary
Summary
This first book to cover all aspects of multi-parametric programming and its applications in process systems engineering includes theoretical developments and algorithms in multi-parametric programming with applications from the manufacturing sector and energy and environment analysis. The volume thus reflects the importance of fundamental research in multi-parametric programming applications, developing mechanisms for the transfer of the new technology to industrial problems. Since the topic applies to a wide range of process systems, as well as due to the interdisciplinary expertise required to solve the challenge, this reference will find a broad readership.
Inspired by the leading authority in the field, the Centre for Process Systems Engineering at Imperial College London.
Author Notes
Efstratios N. Pistikopoulos is a Professor of Chemical Engineering at Imperial College London and Director of its Centre for Process Systems Engineering (PSE). He graduated in Chemical Engineering from Aristotle University of Thessaloniki, Greece and gained a PhD from Carnegie Mellon University, USA. He has authored/ co-authored over 200 publications, holds editorial positions on several editorial boards and has been involved in over 50 major research projects and contracts. Prof. Pistikopoulos is co-founder and Director of two successful spin-off companies stemming from his research at Imperial, Process Systems Enterprise (PSE) Limited and Parametric Optimization Solutions (PAROS) Limited and consults widely to numerous process industry companies.
Michael C. Georgiadis is Head of the Process System Engineering Laboratory at the CPSE, Imperial College London and is the manager for academic business development of Process Systems Enterprise Ltd in Thessaloniki, Greece. He obtained his Chemical Engineering degree from Aristotle University of Thessaloniki, Greece and a MSc and PhD from Imperial College London. Dr. Georgiadis has authored/ co-authored over 55 papers and two books. He has a long experience in the management and participation of more than 20 collaborative research contracts and projects.
Vivek Dua is a Lecturer in the Department of Chemical Engineering at University College London. He holds a degree in Chemical Engineering from Panjab University, Chandigarh, India and MTech in chemical engineering from the Indian Institute of Technology, Kanpur. He joined Kinetics Technology India Ltd. as a Process Engineer before moving to Imperial College London, where he obtained his PhD in Chemical Engineering. He was an Assistant Professor in the Department of Chemical Engineering at Indian Institute of Technology, Delhi before joining University College London. He is a co-founder of Parametric Optimization Solutions (PAROS) Ltd.
Process Systems Enterprise (PSE), provider of the gPROMS advanced process simulation and modelling environment, is the 2007 winner of the Royal Academy of Engineering's MacRobert Award. The award, the UK's most prestigious for engineering, recognises the successful development of innovative ideas. The PSE team was presented with the MacRobert gold medal by HRH Prince Philip.
Table of Contents
Preface-- |
Volume 1 Multiparametric Programming |
List of Authors |
Related Titles |
Part I Theory and Algorithms |
1 Multiparametric Linear and Quadratic Programming |
1.1 Introduction |
1.2 Methodology |
1.3 Numerical Examples |
1.3.1 Example 1: Crude Oil Refinery |
1.3.2 Example 2: Milk Surplus |
1.3.3 Example 3: Model-Based Predictive Contro |
l.1.4 Computational Complexity |
1.5 Concluding Remarks. |
Acknowledgments. |
Appendix A Redundancy Check for a Set of Linear Constraints. |
Appendix B Definition of Rest of the Region. |
Literature |
2 Multiparametric Nonlinear Programming |
2.1 Introduction |
2.1.1 Motivating Example |
2.2 The mp-NLP Algorithm |
2.3 Example |
2.4 Global Optimization Issues |
2.4.1 Remarks and Observations on the Application of the mp-NLP Algorithm for Problem (2.8) |
2.4.2 Algorithm for Multiparametric Nonlinear Programming |
2.4.3 Example (2.8) Solved with the New Algorithm |
2.4.4 Extension to Higher Order Spaces and Higher Order Objective Functions |
2.5 Concluding Remarks. |
Appendix A Infeasibility of Corners. |
Appendix B Comparison Procedure. |
Appendix C Definition of the Rest of the Region. |
Appendix D Redundancy Test. |
Appendix E Vertices of a Critical Region. |
Acknowledgments. |
Literature |
3 Multiparametric Mixed-Integer Linear Programming |
3.1 Parametric Mixed-Integer Linear Programming |
3.2 Multiparametric Mixed-Integer Linear Programming. |
Branch and Bound Approach |
3.3 Multiparametric Mixed-Integer Linear Programming. |
Parametric and Integer Cuts. |
3.3.1 Initialization |
3.3.2 Multiparametric LP Subproblem |
3.3.3 MILP Subproblem |
3.3.4 Comparison of Parametric Solutions |
3.3.5 Multiparametric MILP Algorithm |
3.4 Numerical Example |
3.5 Concluding Remarks. |
Appendix A Definition of an Infeasible Region. |
Literature |
4 Multiparametric Mixed-Integer Quadratic and Nonlinear Programming |
4.1 Introduction |
4.2 Methodology |
4.3 The mp-MIQP Algorithm |
4.3.1 Initialization |
4.3.2 Primal Subproblem |
4.3.3 Master Subproblem |
4.3.4 Strategy for the Solution of the Master Subproblem |
4.3.5 Envelope of Solutions |
4.3.6 Redundant Profiles |
4.4 The mp-MINLP Algorithm |
4.4.1 Initialization |
4.4.2 Primal Subproblem |
4.4.3 Master Subproblem 82 |
4.4.4 Remarks and Summary of the Algorithm |
4.5 Examples |
4.5.1 Example on mp-MIQP |
4.5.2 Example on mp-MINLP |
4.6 Concluding Remarks. |
Acknowledgment. |
Literature |
5 Parametric Global Optimization |
5.1 Introduction |
5.2 Parametric Global Optimization |
5.2.1 B&B Algorithm |
5.2.2 Multiparametric Convex Nonlinear Programs |
5.3 Multiparametric Nonconvex Nonlinear Programming |
5.3.1 Motivating Examples |
5.3.2 An Algorithm for Multiparametric Nonconvex Nonlinear Programming |
5.4 Multiparametric Mixed-Integer Nonconvex Programming |
5.5 Numerical Examples |
5.5.1 Example 1 |
5.5.2 Example 2 |
5.6 Concluding Remarks. |
Acknowledgments. |
Appendix A Comparison of Parametric Solutions. |
Appendix B Definition of Rest of the Region. |
Literature |
6 Bilevel and Multilevel |