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- Optimization in Engineering - OE
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**Thapar University -**- Computer Science Engineering
- B.Tech
- 14 Topics
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- Numerical Optimization Introduction - ( 1 - 44 )
- Historical Development Model Building - ( 45 - 62 )
- Optimization Problem and Model Formation - ( 63 - 72 )
- Classification of Optimization Problems - ( 73 - 79 )
- Classical and Advanced Techniques for Optimization - ( 80 - 84 )
- Classical and Advanced Techniques of Optimization - ( 85 - 89 )
- Stationary Points:Functions of Single and Two Variables - ( 90 - 102 )
- Convexity and Concavity Functions of One and Two Variables - ( 103 - 110 )
- Optimization of Functions of Multiple Variables: Unconstrained Optimization - ( 111 - 114 )
- Optimization of Functions of Multiple Variables Subject to Equality Constraints - ( 115 - 120 )
- Optimization of Function of Multiple Subject to Equality Constraints - ( 121 - 126 )
- Kuhn-Tucker Conditions - ( 127 - 133 )
- Preliminaries - ( 134 - 139 )
- Graphical Method - ( 140 - 145 )

Topic:

Numerical Optimization Introduction Shirish Shevade Computer Science and Automation Indian Institute of Science Bangalore 560 012, India. NPTEL Course on Numerical Optimization Shirish Shevade Numerical Optimization

Introduction Optimization : The procedure or procedures used to make a system or design as effective or functional as possible (adapted from www.thefreedictionary.com) Why Optimization? Helps improve the quality of decision-making Applications in Engineering, Business, Economics, Science, Military Planning etc. Shirish Shevade Numerical Optimization

Mathematical Program Mathematical Program : A mathematical formulation of an optimization problem: Minimize f (x) subject to x ∈ S Essential Components of a Mathematical program: x: variables or parameters f : objective function S: feasible region What is a solution of this Mathematical Program? x ∗ ∈ S such that f (x ∗ ) ≤ f (x) ∀ x ∈ S x ∗ : solution, f (x ∗ ): optimal objective function value x ∗ may not be unique and may not even exist. Maximize f (x) ≡ − Minimize −f (x) Shirish Shevade Numerical Optimization

Mathematical Optimization The problem, Minimize f (x) subject to x ∈ S can be written as min x f (x) s.t. x ∈ S (1) Mathematical Optimization a.k.a. Mathematical programming Study of problem formulations (1), existence of a solution, algorithms to seek a solution and analysis of solutions. Shirish Shevade Numerical Optimization

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