Numerical Optimization

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

Beginner 0(0 Ratings) 0 Students enrolled English
Created by skill expert
Last updated Mon, 20-Jun-2022
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Course overview

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.

Curriculum for this course
41 Lessons 37:39:24 Hours
Lecture
41 Lessons 37:39:24 Hours
  • Introduction
    Preview 00:53:32
  • Mathematical Background
    00:55:44
  • Mathematical Background I
    00:58:51
  • One Dimensional Optimization - Optimality Conditions
    00:56:02
  • One Dimensional Optimization I
    01:08:19
  • Convex Sets
    00:43:58
  • Convex Sets I
    00:56:10
  • Convex Functions II
    00:56:25
  • Convex Functions III
    01:16:29
  • Optimality Conditions, Conceptual Algorithm
    00:36:34
  • Line Search Techniques
    00:57:01
  • Global Convergence Theorem
    00:57:36
  • Steepest Descent Method
    00:57:10
  • Classical Newton Method
    00:57:35
  • Trust Region and Quasi-Newton Methods
    00:57:02
  • Quasi-Newton Methods - Rank One Correction, DFP Method
    00:57:30
  • Quasi-Newton Methods - Rank One Correction, DFP Method I
    00:54:40
  • Conjugate Directions
    00:56:24
  • Quasi-Newton Methods - Rank One Correction, DFP Method II
    00:55:39
  • Constrained Optimization - Local&Global,Conceptual Algorithm
    00:56:57
  • Feasible and Descent Directions
    00:57:03
  • First Order KKT Conditions
    00:58:21
  • Constraint Qualifications
    00:56:33
  • Convex Programming Problem IV
    00:55:19
  • Second Order KKT Conditions
    00:55:10
  • Second Order KKT Conditions 1
    00:50:52
  • Weak and Strong Duality
    00:55:21
  • Geometric Interpretation
    00:55:47
  • Lagrangian Saddle Point and Wolfe Dual
    01:22:31
  • Linear Programming Problem
    00:30:46
  • Geometric Solution
    00:57:22
  • Basic Feasible Solution
    00:57:17
  • Optimality Conditions and Simplex Tableau
    00:57:41
  • Simplex Algorithm and Two-Phase Method
    00:58:00
  • Duality in Linear Programming
    00:58:19
  • Interior Point Methods - Affine Scaling Method
    00:58:10
  • Karmarkars Method
    01:24:30
  • Lagrange Methods, Active Set Method
    00:29:27
  • Active Set Method 1
    00:57:48
  • Barrier& Penalty,Augmented Lagrangian &Cutting Plane Method
    00:32:47
  • Summary
    00:20:42
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