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Computer Science & IT

Numerical Optimization

Numerical Optimization

01 Introduction

02 Mathematical Background

03 Mathematical Background (contd)

04 One Dimensional Optimization - Optimality Conditions

05 One Dimensional Optimization (contd)

07 Convex Sets (contd)

08 Convex Functions

09 Convex Functions (contd)

10 Multi Dimensional Optimization - Optimality Conditions, Conceptual Algorithm

11 Line Search Techniques

12 Global Convergence Theorem

13 Steepest Descent Method

14 Classical Newton Method

15 Trust Region and Quasi-Newton Methods

16 Quasi-Newton Methods - Rank One Correction, DFP Method

17 i) Quasi-Newton Methods - Broyden Family ii) Coordinate Descent Method

18 Conjugate Directions

19 Conjugate Gradient Method

20 Constrained Optimization - Local and Global Solutions, Conceptual Algorithm

21 Feasible and Descent Directions

22 First Order KKT Conditions

23 Constraint Qualifications

24 Convex Programming Problem

25 Second Order KKT Conditions

26 Second Order KKT Conditions (contd)

27 Weak and Strong Duality

28 Geometric Interpretation

29 Lagrangian Saddle Point and Wolfe Dual

30 Linear Programming Problem

31 Geometric Solution

32 Basic Feasible Solution

33 Optimality Conditions and Simplex

34 Simplex Algorithm and Two-Phase Method

35 Duality in Linear Programming

36 Interior Point Methods - Affine Scaling Method

37 Karmarkar's Method

38 Lagrange Methods, Active Set Method

39 Active Set Method (contd)

40 Barrier and Penalty Methods, Augmented Lagrangian Method and Cutting Plane Method

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