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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 17 - Quasi-Newton Methods - Broyden Family; Coordinate Descent Method

Go to the Course Home or watch other lectures:

 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