Numerical Optimization


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