Course teached as: B018804 - OTTIMIZZAZIONE NUMERICA Second Cycle Degree in MATHEMATICS Curriculum APPLICATIVO
Teaching Language
Italiano
Course Content
Main characteristics of numerical methods for unconstrained nonlinear programming. Gradient method, Newton method, line-search techniques. Linear Programming: model formulation, optimality and duality, simplex method, Interior Point methods. Network flow problem. Constrained Nonlinear Optimization: derivation of first order and second order condition. Quadratic
Programming: active set methods, Gradient Projection, Interior Point methods. Basic Fortran instructions. Public domain software for optimization.
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
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other individual formative activities: 153
Contact hours for: Lectures (hours): 50
Contact hours for: Laboratory (hours): 22
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.