Learn · Design and Optimization of Energy systems
Lecture 20 of 40Design and Optimization of Energy systems
Non-linear Regression (Gauss - Newton Algorithm)
Prof. C. Balaji · IIT Madras
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- Design and Optimization of Energy systems, IIT Madras (at NPTEL)
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All the lectures
- Introduction to Optimization
- System Design and Analysis
- Workable system
- System simulation
- Information flow diagrams
- Successive substitution method
- Successive substitution method contd
- Successive substitution method and Newton-Raphson method
- Newton-Raphson method contd
- Convergence characteristics of Newton-Raphson method
- Newton-Raphson method for multiple variables
- Solution of system of linear equations
- Introduction to Curve fitting
- Example for Lagrange interpolation
- Lagrange interpolation contd
- Best fit
- Least Square Regression
- Least Square Regression contd
- Least Square Regression contd
- Non-linear Regression (Gauss - Newton Algorithm)
- Optimization- Basic ideas
- Properties of objective function and cardinal ideas in optimization
- Unconstrained optimization
- Constrained optimization problems
- Mathematical proof of the Lagrange multiplier method
- Test for Maxima/ Minima
- Handling in-equality constraints
- Kuhn-Tucker conditions contd
- Uni-modal function and search methods
- Dichotomous search
- Fibonacci search method
- Reduction ratio of Fibonacci search method
- Introduction to multi-variable optimization
- The Conjugate gradient method
- The Conjugate gradient method contd
- Linear programming
- Dynamic programming
- Genetic Algorithms
- Genetic Algorithms contd
- Simulated Annealing and Summary