Overview of optimization problem, Concepts and terms related to optimization problem, necessary and sufficient conditions, effect of scaling or adding constant to an objective function, constrained and unconstrained optimization problems, Lagrange multiplier, Solution of unconstrained optimization problems using gradient descent method, steepest descent method, Newton's method, DavisonFletcherPowell method and exterior point method, Solution of constrained optimization problems, KarushKuhnTucker (KKT) conditions, convex optimization, quadratic optimization, quadratically constrained quadratic optimization, local and global optima. Solution of quadratic programming problems using KKT conditions, concept of interior penalties and solution of convex optimization problem, simplex method, concepts of multiobjective optimization problem and its solution. Concept of functional, variational problems and performance indices, EulerLagrange equation, Transversality condition, Linear quadratic regulator (LQR) problem, Optimal solution of LQR problem, Solution of algebraic Riccati equation, Frequency domain interpretation of LQR problem, stability and robustness properties of LQR design, dynamic programming principle of optimality, time optimal control problem.
