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Thapar University
**Course:
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B.Tech
**Specialization:
**Computer Science Engineering**Offline Downloads:
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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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