Multi-Parametric Programming Theory, Algorithms and Applications

by Pistikopoulos, Efstratios N.; Georgiadis, Michael C.; Dua, Vivek

• ISBN13: 9783527316915
• ISBN10: 3527316914
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-04-09
• Publisher: Wiley-VCH

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 Biography

Efstratios N. Pistikopoulos is a Professor of Chemical Engineering at Imperial College London and the Director of its Centre for Process Systems Engineering (CPSE). He holds a first degree in Chemical Engineering from Aristotle University of Thessaloniki, Greece and a PhD from Carnegie Mellon University, USA. He has supervised more than twenty PhD students, authored/ co-authored over 150 major research journal publications and been involved in over 50 major research projects and contracts. A co-founder and Director of two successful spin-off companies from Imperial, Process Systems Enterprise (PSE) Limited and Parametric Optimization Solutions (PAROS) Limited, he consults widely to a large number of process industry companies.

Michael C. Georgiadis is a senior researcher in the Centre for Process Systems Engineering at Imperial College London and the manager of academic business development of Process Systems Enterprise Ltd in Thessaloniki, Greece. He holds a first degree in Chemical Engineering from Aristotle University of Thessaloniki and a MSc and PhD from Imperial College. He has authored/ co-authored over 40 journal publications and two books. He has a long experience in the management and participation of more than 20 collaborative research contracts and projects.

Dr. Vivek Dua is a Lecturer in the Department of Chemical Engineering at University College London. He obtained his first 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.

Table of Contents

Preface—

Multiparametric Programming

List of Authors

Related Titles

Theory and Algorithms

Multiparametric Linear and Quadratic Programming

Introduction

Methodology

Numerical Examples

Example 1: Crude Oil Refinery

Example 2: Milk Surplus

Example 3: Model-Based Predictive Contro

Computational Complexity

Concluding Remarks.

Acknowledgments.

Redundancy Check for a Set of Linear Constraints.

Definition of Rest of the Region.

Literature

Multiparametric Nonlinear Programming

Introduction

Motivating Example

The mp-NLP Algorithm

Example

Global Optimization Issues

Remarks and Observations on the Application of the mp-NLP Algorithm for Problem (2.8)

Algorithm for Multiparametric Nonlinear Programming

Example (2.8) Solved with the New Algorithm

Extension to Higher Order Spaces and Higher Order Objective Functions

Concluding Remarks.

Infeasibility of Corners.

Comparison Procedure.

Definition of the Rest of the Region.

Redundancy Test.

Vertices of a Critical Region.

Acknowledgments.

Literature

Multiparametric Mixed-Integer Linear Programming

Parametric Mixed-Integer Linear Programming

Multiparametric Mixed-Integer Linear Programming.

Branch and Bound Approach

Multiparametric Mixed-Integer Linear Programming.

Parametric and Integer Cuts.

Initialization

Multiparametric LP Subproblem

MILP Subproblem

Comparison of Parametric Solutions

Multiparametric MILP Algorithm

Numerical Example

Concluding Remarks.

Definition of an Infeasible Region.

Literature

Multiparametric Mixed-Integer Quadratic and Nonlinear Programming

Introduction

Methodology

The mp-MIQP Algorithm

Initialization

Primal Subproblem

Master Subproblem

Strategy for the Solution of the Master Subproblem

Envelope of Solutions

Redundant Profiles

The mp-MINLP Algorithm

Initialization

Primal Subproblem

Master Subproblem 82

Remarks and Summary of the Algorithm

Examples

Example on mp-MIQP

Example on mp-MINLP

Concluding Remarks.

Acknowledgment.

Literature

Parametric Global Optimization

Introduction

Parametric Global Optimization

B&B Algorithm

Multiparametric Convex Nonlinear Programs

Multiparametric Nonconvex Nonlinear Programming

Motivating Examples

An Algorithm for Multiparametric Nonconvex Nonlinear Programming

Multiparametric Mixed-Integer Nonconvex Programming

Numerical Examples

Example 1

Example 2

Concluding Remarks.

Acknowledgments.

Comparison of Parametric Solutions.

Definition of Rest of the Region.

Literature

Bilevel and Multilevel

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