Students will acquire the basic knowledge in order to model and to solve linear programming problems. Furthermore, they will learn how to apply the basic concepts of nonlinear optimization without constraints.
Course Prerequisites
Linear algebra, Calculus, Numerical Analysis
Teaching Methods
Frontal lessons with theory and exercises.
Assessment Methods
Oral examination and a short project on a topic or an algorithm of the course. The student can choose if deepen a theoretical topic of implement an algorithm. The oral examination will verify the basic tools in optimisation and them application to simple problems.
Contents
Introduction to optimization. Examples and fundamental properties of linear programming. Fundamental theorem of linear programming and its geometric interpretation. Simplex method, block form and revised simplex. Dual problem and primal-dual algorithm. The problem of transport and simplex method for transport problems. Unbounded problems: fundamental properties, methods of descent, steepest discent. Wolf conditions, admissibility and convergence. Stochastic gradient method. Quasi-Newton methods, trust-region method. Levenberg-Marquart method, method of Lagrange multipliers and alternating minimization.
