OPTIMIZATION TECHNIQUES AND APPLICATIONS

UNIT I: Single variable non linear unconstrained optimization:One dimensional minimization methods(248):- Uni-modal function ,elimination methods, unrestricted search, exhaustive search,, Fibonacci method, golden section method, interpolation method.

UNIT II:Multi variable non-linear unconstrained optimization: Direct search method, search methods, invariant method, pattern search method, Rossen - Brocks method of rotating decent methods, gradient of a function(335), steepest decent method(339), Fletcher Reeves method(343), variable metric method.

UNIT III: Geometric programming: Posynomial(492) – arithmetic - geometric inequality(500) – unconstrained G.P(501)- constrained G.P (508). DYNAMIC PROGRAMMING: Multistage decision process(545), principles of optimality(549), examples(555), conversion of final problem to an initial value problem(566), application of dynamic programming(576) , production inventory, allocation, scheduling replacement.

UNIT IV: Linear programming – Formulation – Sensivity analysis(207). Change in the constraints(215), cost coefficients(212), coefficients of the constraints, addition and deletion of variable(214), constraints. Simulation – Introduction – Types- steps – application – inventory – queuing – thermal system. Integer Programming- Introduction(589) – formulation – Gomory cutting plane algorithm(591)– Zero or one algorithm(604), branch and bound method(609)

UNIT V:Stochastic programming:Basic concepts of probability theory(632), random variables(633)- distributions(643)-mean, variance,correlation(640), co variance(640), joint probability distribution(639)- stochastic linear(647), dynamic programming