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Design and Optimization of Energy Systems

Design and Optimization of Energy Systems. Instructor: Prof. C. Balaji, Department of Mechanical Engineering, IIT Madras. This course provides an introduction to design and optimization of energy systems. Topics covered in this course include introduction to system design; regression analysis and curve fitting; modeling of thermal equipment; system simulation (successive substitution, Newton-Raphson method); Lagrange multipliers, search methods, linear programming, geometric programming; simulated annealing, genetic algorithms; examples applied to heat transfer problems and energy systems such as gas and steam power plants, refrigeration systems, heat pumps and so on. (from nptel.ac.in)

Lecture 17 - Least Square Regression


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Lecture 01 - Introduction to Optimization
Lecture 02 - System Design and Analysis
Lecture 03 - Workable System
Lecture 04 - System Simulation
Lecture 05 - Introduction to Flow Diagrams
Lecture 06 - Successive Substitution Method
Lecture 07 - Successive Substitution Method (cont.)
Lecture 08 - Successive Substitution Method and Newton-Raphson Method
Lecture 09 - Newton-Raphson Method (cont.)
Lecture 10 - Convergence Characteristics of Newton-Raphson Method
Lecture 11 - Newton-Raphson Method for Multiple Variables
Lecture 12 - Solution of System of Linear Equations
Lecture 13 - Introduction to Curve Fitting
Lecture 14 - Example for Lagrange Interpolation
Lecture 15 - Lagrange Interpolation (cont.)
Lecture 16 - Best Fit
Lecture 17 - Least Square Regression
Lecture 18 - Least Square Regression (cont.)
Lecture 19 - Least Square Regression (cont.)
Lecture 20 - Nonlinear Regression (Gauss-Newton Algorithm)
Lecture 21 - Optimization: Basic Ideas
Lecture 22 - Properties of Objective Function and Cardinal Ideas in Optimization
Lecture 23 - Unconstrained Optimization
Lecture 24 - Constrained Optimization Problems
Lecture 25 - Mathematical Proof of the Lagrange Multiplier Method
Lecture 26 - Test for Maxima/Minima
Lecture 27 - Handling Inequality Constraints
Lecture 28 - Kuhn-Tucker Conditions
Lecture 29 - Unimodal Function and Search Methods
Lecture 30 - Dichotomous Search
Lecture 31 - Fibonacci Search Method
Lecture 32 - Reduction Ratio of Fibonacci Search Method
Lecture 33 - Introduction to Multivariable Optimization
Lecture 34 - The Conjugate Gradient Method
Lecture 35 - The Conjugate Gradient Method (cont.)
Lecture 36 - Linear Programming
Lecture 37 - Dynamic Programming
Lecture 38 - Genetic Algorithms
Lecture 39 - Genetic Algorithms (cont.)
Lecture 40 - Simulated Annealing and Summary