Contents:
Introduction : Optimization, Types of Problems and Algorithms
Background : Linear Algebra and Analysis,Convex Sets and Convex Functions.

Unconstrained Optimization : Basic properties of solutions and algorithms, Global convergence.

Basic Descent Methods : Line Search Methods, Steepest Descent and Newton Methods,Modified Newton methods, Globally convergent Newton Method,Nonlinear Least Squares Problem and Algorithms,Conjugate Direction Methods,Trust-Region Methods.

Constrained Optimization : First Order Necessary Conditions, Second Order Necessary Conditions, Duality, Constraint Qualification,Convex Programming Problem and Duality.

Linear Programming : The Simplex Method, Duality and Interior Point Methods, Karmarkar’s algorithm,Transportation and Network flow problem.

Dual Methods : Augmented Lagrangians and cutting-plane methods,Penalty and Barrier Methods,Interior Point Methods.

### Course Curriculum

 Introduction Details 53:32 Mathematical Background Details 55:45 Mathematical Background (contd) I Details 58:52 One Dimensional Optimization – Optimality Conditions Details 56:2 One Dimensional Optimization (contd) I Details 1:8:20 Convex Sets Details 43:59 Convex Sets (contd) I Details 56:11 Convex Functions II Details 56:26 Convex Functions (contd) III Details 1:16:30 Multi Dimensional Optimization – Optimality Conditions, Conceptual Algorithm Details 36:35 Line Search Techniques Details 57:1 Global Convergence Theorem Details 57:37 Steepest Descent Method Details 57:11 Classical Newton Method Details 57:36 Trust Region and Quasi-Newton Methods Details 57:3 Quasi-Newton Methods – Rank One Correction, DFP Method Details 57:31 Quasi-Newton Methods – Rank One Correction, DFP Method I Details 54:41 Conjugate Directions Details 56:25 Quasi-Newton Methods – Rank One Correction, DFP Method II Details 55:40 Constrained Optimization – Local and Global Solutions, Conceptual Algorithm Details 56:58 Feasible and Descent Directions Details 57:4 First Order KKT Conditions Details 58:22 Constraint Qualifications Details 56:33 Convex Programming Problem IV Details 55:20 Second Order KKT Conditions Details 55:11 Second Order KKT Conditions (contd) Details 50:53 Weak and Strong Duality Details 55:22 Geometric Interpretation Details 55:48 Lagrangian Saddle Point and Wolfe Dual Details 1:22:33 Linear Programming Problem Details 30:47 Geometric Solution Details 57:23 Basic Feasible Solution Details 57:17 Optimality Conditions and Simplex Tableau Details 57:42 Simplex Algorithm and Two-Phase Method Details 58:1 Duality in Linear Programming Details 58:20 Interior Point Methods – Affine Scaling Method Details 58:10 Karmarkar’s Method Details 1:24:30 Lagrange Methods, Active Set Method Details 29:28 Active Set Method (contd) Details 57:49 Barrier and Penalty Methods, Augmented Lagrangian Method and Cutting Plane Method Details 32:48 Summary Details 20:43

This Course is provided by IISc Bangalore as part of NPTEL online courses.

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