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Numerical Optimization

Numerical Optimization. Instructor: Prof. Shirish K. Shevade, Department of Computer Science and Automation, IISc Bangalore. This course is about studying optimization algorithms, and their applications in different fields.

Mathematical Background: Convex sets and functions, Need for constrained methods in solving constrained problems.
Unconstrained optimization: Optimality conditions, Line Search Methods, Quasi-Newton Methods, Trust Region Methods, Conjugate Gradient Methods, Least Squares Problems.
Constrained Optimization: Optimality Conditions and Duality, Convex Programming Problem, Linear Programming Problem, Quadratic Programming, Dual Methods, Penalty and Barrier Methods, Interior Point Methods. (from nptel.ac.in)

Lecture 18 - Conjugate Directions

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Lecture 01 - Introduction

Mathematical Background

Lecture 02 - Mathematical Background

Lecture 03 - Mathematical Background (cont.)

Unconstrained Optimization

Lecture 04 - One Dimensional Optimization - Optimality Conditions

Lecture 05 - One Dimensional Optimization (cont.)

Convex Sets

Lecture 06 - Convex Sets

Lecture 07 - Convex Sets (cont.)

Convex Functions

Lecture 08 - Convex Functions

Lecture 09 - Convex Functions (cont.)

Unconstrained Optimization

Lecture 10 - Multidimensional 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 - Quasi-Newton Methods - Broyden Family; Coordinate Descent Method

Lecture 18 - Conjugate Directions

Lecture 19 - Conjugate Gradient Method

Constrained Optimization

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 (cont.)

Duality

Lecture 27 - Weak and Strong Duality

Lecture 28 - Geometric Interpretation

Lecture 29 - Lagrangian Saddle Point and Wolfe Dual

Linear Programming

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 - Karmakar's Method

Algorithms for Constrained Optimization Problems

Lecture 38 - Lagrange Method, Active Set Method

Lecture 39 - Active Set Method (cont.)

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

Lecture 41 - Summary