"Convex optimization: Convex set, convex function, conjugate function, directional derivative, sub-gradient, duality theorem. Unconstrained optimization: One-dimensional search algorithms: Fibonacci and golden section search. Multidimensional search method: Steepest descent method, Newton's method, conjugate gradient method, quasi-Newton methods, and trust region method. Constrained optimization: Kuhn-Tucker condition for optimality, application to solution of simple nonlinear problems; quadratic programming and convex programming problems. Penalty and barrier functions. Sequential unconstrained minimization technique, multipliers method."