Optimizations and Programming - El Hami, Abdelkhalak

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Résumé :

Preface xi

Part 1. Programmation 1

Chapter 1. Linear Programming 3

1.1. Introduction 3

1.2. Definitions 3

1.3. Geometry of the linear program 5

1.3.1. Polyhedra 5

1.3.2. Extreme points and vertices 6

1.4. Graphical solving of a linear program 6

1.5. Simplex algorithm 9

1.5.1. Basic solutions and basic feasible solutions 9

1.5.2. Simplex tableau 10

1.5.3. Change of feasible basis 11

1.5.4. Existence and uniqueness of an optimal solution 14

1.6. Initialization of the simplex algorithm 15

1.6.1. Big M method 15

1.6.2. Auxiliary program or Phase I 17

1.6.3. Degeneracy and cycling 20

1.6.4. Geometric structure of realizable solutions 21

1.7. Interior-point algorithm 22

1.8. Duality 23

1.8.1. Duality theorem 25

1.9. Relaxation 27

1.9.1. Lagrangian relaxation 27

1.10. Postoptimal analysis 29

1.10.1. Effect of modifying b 31

1.10.2. Effect of modifying c 32

1.11. Application to an inventory problem 34

1.11.1. Optimal solution 34

1.11.2. Sensitivity to variation in stock 35

1.11.3. Dual problem of the competitor 36

1.12. Using Matlab 36

Chapter 2. Integer Programming 41

2.1. Introduction 41

2.2. Solving methods 41

2.2.1. Branch-and-bound method 42

2.2.2. The branch-and-cut method 44

2.3. Binary programming 49

2.3.1. Knapsack problem 49

2.3.2. Investment problem 50

2.4. Decomposition principle 57

2.4.1. Benders decomposition 58

2.5. Using Matlab 62

Chapter 3. Dynamic Programming 65

3.1. Introduction 65

3.2. Solving strategy 66

3.3. Discrete DP 68

3.3.1. Bellman's equation and the principle of optimality 68

3.3.2. Approach of the method 70

3.3.3. A few examples of DP 70

3.3.4. Solving an LP 73

3.3.5. Shortest path problem 74

3.3.6. Knapsack problem 79

3.3.7. Stock management problem 81

3.4. Continuous DP 83

3.4.1. Hamilton-Jacobi equation 84

3.4.2. Application to a consumption-savings model 84

3.5. Stochastic DP 85

3.5.1. Decision-chance process 85

3.5.2. Solving method 86

3.5.3. Application to a contract problem 86

3.5.4. Optimal binary search tree 87

3.6. Using Matlab 91

Chapter 4. Stochastic Programming 93

4.1. Introduction 93

4.2. Presentation of the problem 94

4.3. Optimal feedback in an open loop 94

4.4. Stochastic linear programming 95

4.4.1. Models with probability thresholds on the constraints 96

4.5. Stochastic linear programs with recourse 96

4.5.1. L-shaped method 97

4.5.2. Multicut L-shaped method 99

4.5.3. Interior linearization method 100

4.6. Nonlinear stochastic programming 100

4.6.1. Approaches to two-step problems with recourse 100

4.6.2. Regularized decomposition method 101

4.6.3. Methods based on the Lagrangian 101

4.6.4. Frank-Wolfe method for problems with simple recourse 103

4.6.5. Approximation by sampling average: Monte Carlo method 105

4.6.6. Stochastic gradient method 106

4.7. Stochastic dynamic programming 107

4.7.1. Markov decision process 108

4.7.2. Scenario tree 109

4.8. Application to the reliability of mechanical systems 111

4.8.1. Position and modeling of the reliability problem 113

4.9. Using Matlab 121

Part 2. Optimization 127

Chapter 5. Combinatorial Optimization 129

5.1. Introduction 129

5.2. Symmetric TSP 131

5.2.1. His...

Biographie:

Abdelkhalak El Hami is Full Professor of Universities at INSA-RouenNormandie, France. He is the author/co-author of several books and is responsible for the Chair of mechanics at the Conservatoire National des Arts et M?tiers in Normandy, as well as for several European pedagogical projects. He is a specialist in problems of optimization and reliability in multi-physical systems.

Boucha?b Radi is Professor at the Faculty of Science and Technology at Hassan Premier University, Morocco. He is a specialist in numerical optimization methods and system reliability....

Sommaire:

This book is a general presentation of complex systems, examined from the point of view of management. There is no standard formula to govern such systems, nor to effectively understand and respond to them.

The interdisciplinary theory of self-organization is teeming with examples of living systems that can reorganize at a higher level of complexity when confronted with an external challenge of a certain magnitude. Modern businesses, considered as complex systems, ideally know how to flexibly and resiliently adapt to their environment, and also how to prepare for change via self-organization. Understanding sources of potential crisis is essential for leaders, though not all crises are necessarily bad news, as creative firms know how to respond to challenges through innovation: new products and markets, organizational learning for collective intelligence, and more....