Table of Contents 1
Cover
5
PART 1: Programmation
1 Linear Programming
1.1. Introduction
1.2. Definitions
1.3. Geometry of the linear program
1.4. Graphical solving of a linear program
1.5. Simplex algorithm
1.6. Initialization of the simplex algorithm
1.7. Interior-point algorithm
1.8. Duality
1.9. Relaxation
1.10. Postoptimal analysis
1.11. Application to an inventory problem
1.12. Using Matlab
2 Integer Programming
2.1. Introduction
2.2. Solving methods
2.3. Binary programming
2.4. Decomposition principle
2.5. Using Matlab
3 Dynamic Programming
3.1. Introduction
3.2. Solving strategy
3.3. Discrete DP
3.4. Continuous DP
3.5. Stochastic DP
3.6. Using Matlab
4 Stochastic Programming
4.1. Introduction
4.2. Presentation of the problem
4.3. Optimal feedback in an open loop
4.4. Stochastic linear programming
4.5. Stochastic linear programs with recourse
4.6. Nonlinear stochastic programming
4.7. Stochastic dynamic programming
4.8. Application to the reliability of mechanical systems
4.9. Using Matlab
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PART 2: Optimization
5 Combinatorial Optimization
5.1. Introduction
5.2. Symmetric TSP
5.3. Asymmetric traveling salesman problem
5.4. Vehicle routing problem
5.5. Selective routing problem
5.6. Using Matlab
6 Unconstrained Nonlinear Programming
6.1. Introduction
6.2. Mathematical formulation
6.3. Optimality conditions
6.4. Quadratic problems
6.5. Newton’s algorithm
6.6. Methods of descent and linear search
6.7. Quasi-Newton methods
6.8. Relaxation method
6.9. Gradient method
6.10. Least squares problem
6.11. Direct search methods
6.12. Application to an identification problem
6.13. Using Matlab
7 Constrained Nonlinear Optimization
7.1. Introduction
7.2. Mathematical formulation
7.3. Lagrange multipliers
7.4. Optimization with inequality constraints
7.5. Constrained minimization algorithms
7.6. Newton algorithms: SQP method
7.7. Application to structure optimization
7.8. Using Matlab
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Appendices
Appendix 1: Reminders from Linear Algebra
A1.1. Vector space
A1.2. Linear mappings
A1.3. Matrices
A1.4. Determinants
A1.5. Scalar product
