Читать книгу Optimizations and Programming - Bouchaib Radi, Ghias Kharmanda, Michel Ledoux - Страница 2

1  Cover

2  Title Page

3  Copyright

4  Preface Acknowledgments

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

6  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

7  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 A1.6. Vector norm Appendix 2: Reminders about functions from ℝn into ℝ A2.1. Differentiability A2.2. Convexity A2.3. Quadratic function Appendix 3: Optimization Toolbox A3.1. Introduction A3.2. Various functions A3.3. Matlab’s optimization application Appendix 4: Software A4.1. Autonomous and multipurpose optimization software A4.2. Packages for specific classes of problems A4.3. Optimization software for design A4.4. Solvers for stochastic optimization

8  References

9  Index

10  End User License Agreement