Numerical Optimization

IISc Bangalore Course , Prof. Shirish K. Shevade

Lecture 1: Introduction

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Lecture Details :

Numerical Optimization by Dr. Shirish K. Shevade, Department of Computer Science and Engineering, IISc Bangalore. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

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.

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

These lecture videos are delivered by IISc Bangalore, under the NPTEL program, lot of nptel video courses are available for learning online.

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