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.

Quadratic Programming : Active set methods, Gradient Projection methods and sequential quadratic programming.
Dual Methods : Augmented Lagrangians and cutting-plane methods,Penalty and Barrier Methods,Interior Point Methods.

Other Resources

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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