Introduction : Optimization, Types of Problems and Algorithms
Background : Linear Algebra and Analysis,Convex Sets and Convex Functions.
Unconstrained Optimization : Basic properties of solutions and algorithms, Global convergence.
Basic Descent Methods : Line Search Methods, Steepest Descent and Newton Methods,Modified Newton methods, Globally convergent Newton Method,Nonlinear Least Squares Problem and Algorithms,Conjugate Direction Methods,Trust-Region Methods.
Constrained Optimization : First Order Necessary Conditions, Second Order Necessary Conditions, Duality, Constraint Qualification,Convex Programming Problem and Duality.
Linear Programming : The Simplex Method, Duality and Interior Point Methods, Karmarkar’s algorithm,Transportation and Network flow problem.
Quadratic Programming : Active set methods, Gradient Projection methods and sequential quadratic programming.
Dual Methods : Augmented Lagrangians and cutting-plane methods,Penalty and Barrier Methods,Interior Point Methods.
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