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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