Learn · Numerical Optimization
Lecture 5 of 41Unconstrained Optimization
One Dimensional Optimization (contd)
Dr. Shirish K. Shevade · IISc Bangalore
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- Numerical Optimization, IISc Bangalore (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Introduction
- Mathematical Background
- Mathematical Background (contd)
- One Dimensional Optimization - Optimality Conditions
- One Dimensional Optimization (contd)
- Convex Sets
- Convex Sets (contd)
- Convex Functions
- Convex Functions (contd)
- Multi Dimensional Optimization - Optimality Conditions, Conceptual Algorithm
- Line Search Techniques
- Global Convergence Theorem
- Steepest Descent Method
- Classical Newton Method
- Trust Region and Quasi-Newton Methods
- Quasi-Newton Methods - Rank One Correction, DFP Method
- i) Quasi-Newton Methods - Broyden Family ii) Coordinate Descent Method
- Conjugate Directions
- Conjugate Gradient Method
- Constrained Optimization - Local and Global Solutions, Conceptual Algorithm
- Feasible and Descent Directions
- First Order KKT Conditions
- Constraint Qualifications
- Convex Programming Problem
- Second Order KKT Conditions
- Second Order KKT Conditions (contd)
- Weak and Strong Duality
- Geometric Interpretation
- Lagrangian Saddle Point and Wolfe Dual
- Linear Programming Problem
- Geometric Solution
- Basic Feasible Solution
- Optimality Conditions and Simplex Tableau
- Simplex Algorithm and Two-Phase Method
- Duality in Linear Programming
- Interior Point Methods - Affine Scaling Method
- Karmarkar\'s Method
- Lagrange Methods, Active Set Method
- Active Set Method (contd)
- Barrier and Penalty Methods, Augmented Lagrangian Method and Cutting Plane Method
- Summary