تکنیک های بهینه سازی I ۲۰۲۳
Optimization techniques I 2023

1. Preface

2. Introduction

3. Table of contents

1. Continuous optimization

5. Introduction

1.1 Formulation

1.2 Numerical derivatives

1.3 Problem reduction

1.4 Global optimum

1.5 Local optimum

1.6 Conclusion

2. Gradient-free optimization

13. Introduction

2.1 Difficult optimization

2.2 One-dimensional optimization

2.3 DIRECT method

2.4 Nelder-Mead method

2.5 Affine shaker

2.6 CMAES

2.7 Simulated annealing

2.8 Research with tabu

2.9 Particle swarms

2.10 Ant colonies

2.11 Evolutionary algorithms

2.12 Conclusion

3. Unconstrained optimization

27. Introduction

3.1 Newton’s method

3.2 Quasi-Newton methods

3.3 Line search

3.4 Trust region

3.5 Proximal methods

3.6 Convergence

3.7 Conclusion

4. Constrained optimization

36. Introduction

4.1 Classification of methods

4.2 Penalization

4.3 Reduced gradient

4.4 Sequential quadratic programming

4.5 Interior point

4.6 Augmented Lagrangian

4.7 Conclusion

5. Linear programming

45. Introduction

5.1 Simplex

5.2 Interior point

5.3 Conclusion

49. Index

50. Bibliography