Computer - Numerical Optimization (English)

4    Wednesday, March 19, 2025   

Starting a new Lecture Notes Series on Computer - Numerical Optimization

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Computer - Numerical Optimization By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Introduction

Lecture 2: Mod-02 Lec-02 Mathematical Background

Lecture 3: Mod-02 Lec-03 Mathematical Background (contd)

Lecture 4: Mod-03 Lec-04 One Dimensional Optimization - Optimality Conditions

Lecture 5: Mod-03 Lec-05 One Dimensional Optimization (contd)

Lecture 6: Mod-04 Lec-06 Convex Sets

Lecture 7: Mod-04 Lec-07 Convex Sets (contd)

Lecture 8: Mod-05 Lec-08 Convex Functions

Lecture 9: Mod-05 Lec-09 Convex Functions (contd)

Lecture 10: Mod-06 Lec-10 Multi Dimensional Optimization - Optimality Conditions, Conceptual Algorithm

Lecture 11: Mod-06 Lec-11 Line Search Techniques

Lecture 12: Mod-06 Lec-12 Global Convergence Theorem

Lecture 13: Mod-06 Lec-13 Steepest Descent Method

Lecture 14: Mod-06 Lec-14 Classical Newton Method

Lecture 15: Mod-06 Lec-15 Trust Region and Quasi-Newton Methods

Lecture 16: Mod-06 Lec-16 Quasi-Newton Methods - Rank One Correction, DFP Method

Lecture 17: Mod-06 Lec-17 Quasi-Newton Methods - Rank One Correction, DFP Method

Lecture 18: Mod-06 Lec-18 Conjugate Directions

Lecture 19: Mod-06 Lec-19 Quasi-Newton Methods - Rank One Correction, DFP Method

Lecture 20: Mod-07 Lec-20 Constrained Optimization - Local and Global Solutions, Conceptual Algorithm

Lecture 21: Mod-07 Lec-21 Feasible and Descent Directions

Lecture 22: Mod-07 Lec-22 First Order KKT Conditions

Lecture 23: Mod-07 Lec-23 Constraint Qualifications

Lecture 24: Mod-07 Lec-24 Convex Programming Problem

Lecture 25: Mod-07 Lec-25 Second Order KKT Conditions

Lecture 26: Mod-07 Lec-26 Second Order KKT Conditions (contd)

Lecture 27: Mod-08 Lec-27 Weak and Strong Duality

Lecture 28: Mod-08 Lec-28 Geometric Interpretation

Lecture 29: Mod-08 Lec-29 Lagrangian Saddle Point and Wolfe Dual

Lecture 30: Mod-09 Lec-30 Linear Programming Problem

Lecture 31: Mod-09 Lec-31 Geometric Solution

Lecture 32: Mod-09 Lec-32 Basic Feasible Solution

Lecture 33: Mod-09 Lec-33 Optimality Conditions and Simplex Tableau

Lecture 34: Mod-09 Lec-34 Simplex Algorithm and Two-Phase Method

Lecture 35: Mod-09 Lec-35 Duality in Linear Programming

Lecture 36: Mod-09 Lec-36 Interior Point Methods - Affine Scaling Method

Lecture 37: Mod-09 Lec-37 Karmarkar's Method

Lecture 38: Mod-10 Lec-38 Lagrange Methods, Active Set Method

Lecture 39: Mod-10 Lec-39 Active Set Method (contd)

Lecture 40: Mod-10 Lec-40 Barrier and Penalty Methods, Augmented Lagrangian Method and Cutting Plane Method

Lecture 41: Mod-10 Lec-41 Summary