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Course10610805641 lectures

Numerical Optimization

Dr. Shirish K. Shevade · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Introduction

  1. Introduction Video

Mathematical Background

  1. Mathematical Background Video
  2. Mathematical Background (contd) Video

Unconstrained Optimization

  1. One Dimensional Optimization - Optimality Conditions Video
  2. One Dimensional Optimization (contd) Video

Convex Sets

  1. Convex Sets Video
  2. Convex Sets (contd) Video

Convex Functions

  1. Convex Functions Video
  2. Convex Functions (contd) Video

Unconstrained Optimization.

  1. Multi Dimensional Optimization - Optimality Conditions, Conceptual Algorithm Video
  2. Line Search Techniques Video
  3. Global Convergence Theorem Video
  4. Steepest Descent Method Video
  5. Classical Newton Method Video
  6. Trust Region and Quasi-Newton Methods Video
  7. Quasi-Newton Methods - Rank One Correction, DFP Method Video
  8. i) Quasi-Newton Methods - Broyden Family ii) Coordinate Descent Method Video
  9. Conjugate Directions Video
  10. Conjugate Gradient Method Video

Constrained Optimization

  1. Constrained Optimization - Local and Global Solutions, Conceptual Algorithm Video
  2. Feasible and Descent Directions Video
  3. First Order KKT Conditions Video
  4. Constraint Qualifications Video
  5. Convex Programming Problem Video
  6. Second Order KKT Conditions Video
  7. Second Order KKT Conditions (contd) Video

Duality

  1. Weak and Strong Duality Video
  2. Geometric Interpretation Video
  3. Lagrangian Saddle Point and Wolfe Dual Video

Linear Programming

  1. Linear Programming Problem Video
  2. Geometric Solution Video
  3. Basic Feasible Solution Video
  4. Optimality Conditions and Simplex Tableau Video
  5. Simplex Algorithm and Two-Phase Method Video
  6. Duality in Linear Programming Video
  7. Interior Point Methods - Affine Scaling Method Video
  8. Karmarkar\'s Method Video

Algorithms for Constrained Optimization Problems

  1. Lagrange Methods, Active Set Method Video
  2. Active Set Method (contd) Video
  3. Barrier and Penalty Methods, Augmented Lagrangian Method and Cutting Plane Method Video
  4. Summary Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Computer Science and Engineering
Teacher
Dr. Shirish K. Shevade
Level
Undergraduate
Language
English
Subjects
Computer science, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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