UNIT - I Introduction and Classical Optimization Techniques : Statement of an Optimization problem - design vector - design constraints - constraint surface - objective function - objective function surfaces - classification of Optimization problems. Classical Optimization Techniques : Single variable Optimization - multi variable Optimization without constraints - necessary and sufficient conditions for minimum/maximum - multivariable Optimization with equality constraints. Solution by method of Lagrange multipliers - Multivariable Optimization with inequality constraints - Kuhn - Tucker conditions. (Chapters - 1, 2) UNIT - II Linear Programming : Standard form of a linear programming problem – geometry of linear programming problems - definitions and theorems - solution of a system of linear simultaneous equations - pivotal reduction of a general system of equations - motivation to the simplex method - simplex algorithm. Transportation Problem : Finding initial basic feasible solution by north - west corner rule, least cost method and Vogel’s approximation method - testing for optimality of balanced transportation problems. (Chapters - 3, 4) UNIT – III Unconstrained Nonlinear Programming : One dimensional minimization methods, Classification, Fibonacci method and Quadratic interpolation method Unconstrained Optimization Techniques: Univariant method, Powell’s method and steepest descent method. (Chapters - 5, 6) UNIT - IV Constrained Nonlinear Programming : Characteristics of a constrained problem - classification - Basic approach of Penalty Function method - Basic approach of Penalty Function method - Basic approaches of Interior and Exterior penalty function methods - Introduction to convex programming problem. (Chapter - 7) UNIT - V Dynamic Programming : Dynamic programming multistage decision processes - types - concept of sub optimization and the principle of optimality - computational procedure in dynamic programming - examples illustrating the calculus method of solution - examples illustrating the tabular method of solution. (Chapter - 8)
