Course teached as: B018804 - OTTIMIZZAZIONE NUMERICA Second Cycle Degree in MATHEMATICS Curriculum GENERALE
Teaching Language
Italian
Course Content
Main characteristics of numerical methods for unconstrained nonlinear programming. Optimality conditions for constrained optimization. Methods for Linear and Quadratic Programming problems. Basic Fortran instructions. Public domain software.
J. Nocedal, S.J. Wright, "Numerical Optimization", 2nd ed., 2006
Learning Objectives
Knowledge of optimality theory for linear programming and constrained nonlinear programming.
Knowledge of the main numerical optimization methods for linear and constrained nonlinear programming and of their theoretical background.
Prerequisites
Courses recommended: first level courses of Mathematical Analysis and Numerical Analysis
Teaching Methods
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Sessions in the computer lab with the aim of:
- Learning of Fortran programming language and implementation of methods for unconstrained optimization presented during the lectures;
-use of software packages for constrained problems and numerical resolution of problems arising in engineering applications.
Type of Assessment
Oral test about lecture’s topics and laboratory activities.
Course program
Unconstrained nonlinear programming: optimality conditions, gradient method, Newton method. Line-search globalization techniques. Use of public domain software.
Linear Programming: models formulation with examples from optimal resource allocation,
transportation problems.
Introduction to Linear programming: Basic Feasible points, feasible polytope, Optimality and Duality Theory, simplex method.
Primal Dual Interior Point methods: Introduction, central path, path-following methods: convergence theory . Public domain software for linear programming .
Network flow problems: minimum cost path, max flow problems, max-flow-min-cut, Ford e Fulkerson Algorithm.
Constrained Nonlinear Optimization: models formulation with examples,
feasible directions, derivation of first order and second order conditions
Quadratic Programming: active set method, Gradient
Projection methods , Extension of Interior Point methods to Quadratic Programming
Introduction to Fortran language: basic instructions, subroutines, libraries.