Introduction to Optimization: Engineering application of Optimization – Statement of an optimization problem- Optimal Problem formulation – Classification of optimization problems. Definition of Global and Local minima. Unconstrained Optimization: Optimality Conditions- Algorithms for univariate optimization- Algorithms for multivariate optimization- Convergence of algorithms – Engineering applications of unconstrained algorithms. Lagrange multiplier Theory & Duality: Lagrange Multipliers- Kuhn- Tucker Optimality Conditions and sufficiency for convex problems- Lagrangian duality- Saddle point conditions. Constrained Optimization: Optimality conditions- Feasible direction methods- Frank- Wolfe algorithm- Gradient Projection – Active set methods- Penalty function methods- Constrained steepest descent method. Modern methods of optimization: Genetic Algorithms- Simulated Annealing – Tabu search – Ant Colony optimization – Particle Swarm Optimization – Neural- Network based Optimization – Fuzzy optimization techniques. Introduction to Multi – Objective optimization – Classical methods- Pareto Optimality – Use of evolutionary algorithms for solving Multi Objective optimization problems. – Lab Practice: Use of programming languages and Matlab to solve optimization problems.