Optimization problem formulation - Design variables, constraints, objective function and variable; bounds. Single-Variable ; Single Variable Optimization Algorithm: Bracketing Melliotls Exhaustive Search Method and bounding; Phase Method. ; Region Elimination Methods: Fibonacci Search method and Golden section search method. Gradient based ; methods, Newton - Raphson method, Bisection Method, Secant Method, and Cubic Search Method. Computer programs for bounding phase method and golden section search method; Multivariable Optimization Algorithms: Direct search methods. Simplex search method and Hooke- Jeeves pattern search method. Gradient based methods, Constrained Optimization Algorithms- Kuhn- Tucker conditions, penalty function. Method, method of multipliers, cutting plane method, Generalized Reduced Gradient method, computer program for penalty function method. Integer programming - penalty function method. Global optimization using the steepest descent method, genetic algorithms and simulated annealing.