Table of Contents
1 Cover
6 Short Bios of the Authors Efstratios N. Pistikopoulos Nikolaos A. Diangelakis Richard Oberdieck
7 Preface
8
Part I Multi‐parametric Optimization
1 Introduction
1.1 Concepts of Optimization
1.2 Concepts of Multi‐parametric Programming
1.3 Polytopes
1.4 Organization of the Book
References
Notes
2 Multi‐parametric Linear Programming
2.1 Solution Properties
2.2 Degeneracy
2.3 Critical Region Definition
2.4 An Example: Chicago to Topeka
2.5 Literature Review
References
Notes
3 Multi‐Parametric Quadratic Programming
3.1 Calculation of the Parametric Solution
3.2 Solution Properties
3.3 Chicago to Topeka with Quadratic Distance Cost
3.4 Literature Review
References
Notes
4 Solution Strategies for mp‐LP and mp‐QP Problems
4.1 General Overview
4.2 The Geometrical Approach
4.3 The Combinatorial Approach
4.4 The Connected‐Graph Approach
4.5 Discussion
4.6 Literature Review
References
Notes
5 Multi‐parametric Mixed‐integer Linear Programming
5.1 Solution Properties
5.2 Comparing the Solutions from Different mp‐LP Problems
5.3 Multi‐parametric Integer Linear Programming
5.4 Chicago to Topeka Featuring a Purchase Decision
5.5 Literature Review
References
Notes
6 Multi‐parametric Mixed‐integer Quadratic Programming
6.1 Solution Properties
6.2 Comparing the Solutions from Different mp‐QP Problems
6.3 Envelope of Solutions
6.4 Chicago to Topeka Featuring Quadratic Cost and A Purchase Decision
6.5 Literature Review
References
Notes
7 Solution Strategies for mp‐MILP and mp‐MIQP Problems
7.1 General Framework
7.2 Global Optimization
7.3 Branch‐and‐Bound
7.4 Exhaustive Enumeration
7.5 The Comparison Procedure
7.6 Discussion
7.7 Literature Review
References
Notes
8 Solving Multi‐parametric Programming Problems Using MATLAB®
8.1 An Overview over the Functionalities of POP
8.2 Problem Solution
8.3 Problem Generation
8.4 Problem Library
8.5 Graphical User Interface (GUI)
8.6