Optimization- Theory and Application

 
OPTIMIZATION - THEORY AND APPLICATIONS 


Group A
Introduction to optimisation: Hist orical development. Engineering applications. Statement of
an optimisation problem, classification and formulation of optimisation problems,
optimisation techniques.
Classical optimisation methods: Single variable optimisation, multivaria ble optimisation with
and without constraints.
Linear programming: Standard form of a li near programming problem (LPP), geometry of
LPPs, related theorems, linear simultaneous equations, pivo tal reduction, simplex method,
revised simplex method, duality, decomposition,  transportation and assignment problems.
Nonlinear programming (unconstrained): Uni-m odal function, exhaustive search, bi-section
and golden section methods, interpolation me thods, random search methods, univariate
method, gradient of a function, conjugate gradient, quasi-N ewton and variable metric
methods. 



Group B
Nonlinear programming (constrained): Complex method* cutting plane method, method of
feasible directions, transformation techni ques, penalty function methods, convergence
checks.
Geometric programming: Introduction to geometric programming, polynomial, unconstrained
and constrained problems.
Dynamic programming: Introduction to dyn amic programming, multistage decision
processes, computational procedur es, calculus and tabular methods.

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