NPTEL : Numerical Optimization (Computer Science and Engineering)

Co-ordinators : Dr. Shirish K. Shevade


Lecture 1 - Introduction

Lecture 2 - Mathematical Background

Lecture 3 - Mathematical Background (Continued...)

Lecture 4 - One Dimensional Optimization - Optimality Conditions

Lecture 5 - One Dimensional Optimization (Continued...)

Lecture 6 - Convex Sets

Lecture 7 - Convex Sets (Continued...)

Lecture 8 - Convex Functions

Lecture 9 - Convex Functions (Continued...)

Lecture 10 - Multi Dimensional Optimization - Optimality Conditions, Conceptual Algorithm

Lecture 11 - Line Search Techniques

Lecture 12 - Global Convergence Theorem

Lecture 13 - Steepest Descent Method

Lecture 14 - Classical Newton Method

Lecture 15 - Trust Region and Quasi-Newton Methods

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

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

Lecture 18 - Conjugate Directions

Lecture 19 - Conjugate Gradient Method

Lecture 20 - Constrained Optimization - Local and Global Solutions, Conceptual Algorithm

Lecture 21 - Feasible and Descent Directions

Lecture 22 - First Order KKT Conditions

Lecture 23 - Constraint Qualifications

Lecture 24 - Convex Programming Problem

Lecture 25 - Second Order KKT Conditions

Lecture 26 - Second Order KKT Conditions (Continued...)

Lecture 27 - Weak and Strong Duality

Lecture 28 - Geometric Interpretation

Lecture 29 - Lagrangian Saddle Point and Wolfe Dual

Lecture 30 - Linear Programming Problem

Lecture 31 - Geometric Solution

Lecture 32 - Basic Feasible Solution

Lecture 33 - Optimality Conditions and Simplex Tableau

Lecture 34 - Simplex Algorithm and Two-Phase Method

Lecture 35 - Duality in Linear Programming

Lecture 36 - Interior Point Methods - Affine Scaling Method

Lecture 37 - Karmarkar's Method

Lecture 38 - Lagrange Methods, Active Set Method

Lecture 39 - Active Set Method (Continued...)

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

Lecture 41 - Summary