Theory of Optimization by Ma'am Iqra Razzaq

These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Thease notes are based on the lectures by Ma'am Iqra Razzaq.

• Introduction
• Formal definition
• Status of Optimization
• Flow chart of Modeling process
• Requirement of Optimization Algorithm
• Types of Optimization
• Constraints
• Convex Function
• Convex Optimization Problem
• Matrix form of equations
• Hessian matrix method
• Unconstraint Optimization problems
• Principle minor diagonal
• Newton Raphson Method (For unconstraint’s Optimization)
• Non-linear programming
• Local and Global optima
• Results from Calculus
• Three-point interval search
• Fibonacci Search method
• Mean Search or Golden Mean search or Golden section search method
• The method of steepest Ascent
• Nelder Mead Method
• Fletcher-Powell Method
• Lagrange Multiplier Method
• Single Constraint
• Multiple Constraints
• Newton Raphson’s Method of constraint optimization (for equally constraints)
• Karush-Kuhn-Tucker Method

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