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
