Continuous Optimization

Course objectives

The course introduces to the nonlinear continuous optimization problems and describes the main methodological approaches to efficiently solve this class of optimization problems. At the end of the course, the student should be able to identify the most suitable methodological approach to tackle the real problem to be solved [A) knowledge and understanding]. The student should also be able to correctly use the software available in literature and/or to realize new codes for solving nonlinear continuous optimization problems [B) applying knowledge and understanding]. The student should also have the ability to integrate the mathematical tools proposed in the course to tackle complex real problems [ C) making judgements]. The student should also show that he / she is able to communicate and transfer the methodological approaches used in the considered problems [ D) communication skills]. Finally, the student should have learned well the concepts and methodologies proposed in the course that allow him / her to independently deep further methodological developments of Continuous Optimization [ E) learning skills]. The skills achieved by the student will be verified by a written exam.

Channel 1
STEFANO LUCIDI Lecturers' profile

Program - Frequency - Exams

Course program
1. Introduction to continuous optimization problems: definitions, preliminary results, examples, applications and mathematical characterizations of the solutions. 2. Local optimization methods: general characterizations and properties, unconstrained optimization methods (gradient method, Newton method, conjugate gradient methods, Quasi-Newton methods, ,derivative free methods), constrained optimization methods (penalty functions, recursive quadratic programming methods). 3. Global optimization methods: general characterizations and properties, stochastic methods (random sampling methods, multi start methods, simulated annealing methods, controlled random search, genetic algorithms, evolutionary algorithms.
Prerequisites
The basic notions of linear algebra and of the geometry of the real n dimensional space are to be considered indispensable prerequisites.
Books
The material is made available on the course website by the teacher. This material consists of handouts suitably prepared by the teacher, that report all the topics covered in the lessons and a collection of solved exercises and exam exercises. In addition, ongoing self-assessment tests will be offered to the students.
Teaching mode
The teaching model includes lectures and collective exercises.
Frequency
Optional
Exam mode
The exam test consists of - a written test (2 hours development time) with a closed stimulus and an open answer that aims both to verify the student’s knowledge of the theoretical topics of the course and his ability to apply the proposed methodologies through the exercises The final evaluation is attributed based on the correction of the written tests and the discussion of the these tests with the student.
Lesson mode
The teaching model includes lectures and collective exercises.
  • Lesson code1047553
  • Academic year2024/2025
  • CourseManagement Engineering
  • CurriculumModelli decisionali per l'Ingegneria gestionale
  • Year1st year
  • Semester2nd semester
  • SSDMAT/09
  • CFU6
  • Subject areaAttività formative affini o integrative