MSc: Optimization
Optimization
- Course name: Optimization
- Course number: R-01
Course characteristics
Key concepts of the class
- Optimization of a cost function
- Algorithms to find solution of linear and nonlinear optimization problems
What is the purpose of this course?
The main purpose of this course to make the student aware of basic notions of mathematical programming and of its importance in the area of engineering.
Course Objectives Based on Bloom’s Taxonomy
What should a student remember at the end of the course?
By the end of the course, the students should be able to
- explain the goal of an optimization problem
- remind the importance of converge analysis for optimization algorithms
- draft solution codes in Python/Matlab.
What should a student be able to understand at the end of the course?
By the end of the course, the students should be able to
- formulate a simple optimization problem
- select the appropriate solution algorithm
- find the solution.
What should a student be able to apply at the end of the course?
By the end of the course, the students should be able to apply:
- the simplex method
- algorithms to solve nonlinear optimization problems.
Course evaluation
The course has two major forms of evaluations:
- a standard evaluation,
- for very motivated students, an alternative form of evaluation.
The standard evaluation follows.
| Component | Points |
|---|---|
| Labs/seminar classes (weekly evaluations) | 30 0 |
| Interim performance assessment (class participation) | 5 |
| Exams | 65 2 |
1 Of which 15 for online test done during the tutorial, 15 for homeworks related to labs.
2 Of which 35% for the written and 30% for the oral.
Succi Giancarlo, [03.11.21 17:48] Note: A student who has earned 70% of the grade before the oral exam (meaning 49% of the total grade), can apply for exemption to such oral exam, unless explicitly required by the instructor to take it, at full discretion of the instructor. In such case the grade final grade is computed as follows: all the grades below a total of 55% will award a C and all the one from 55% onward (up to 70%) will award a B. A student aiming at an A in the course has to do the oral exam.
The alternative evaluation follows.
The alternative form of evaluation assumes attendance to all lecture and always a grade above 9/10 or equivalent. Students interested to opt for this approach need to inform Xavier Vasquez about their choice no later than during the third Tutorial (1st September). If during the semester a student fails to satisfy the criteria for taking the alternative form of evaluation, s/he is automatically reverted to the standard evaluation.
| Component | Points |
|---|---|
| Labs/seminar classes (weekly evaluations) | 20 1 |
| Interim performance assessment (class participation) | 5 |
| Solutions to questions of Bach directly in the text | 50 |
| Exams | 25 2 |
Grades range
| A. Excellent | 96-100 |
| B. Good | 66-95 |
| C. Satisfactory | 56-65 |
| D. Poor | 0-55 |
Resources and reference material
- Textbook: C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization, Dover, New York, 1982.
- Textbook: D. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.
Course Sections
The main sections of the course and approximate hour distribution between them is as follows:
| Section | Section Title | Teaching Hours |
|---|---|---|
| 1 | Linear programming | 15 |
| 2 | Nonlinear programming | 15 |
Section 1
Section title: Linear programming
Topics covered in this section
- simplex method to solve real linear programs
- cutting-plane and branch-and-bound methods to solve integer linear programs.
What forms of evaluation were used to test students’ performance in this section?
| Yes/No | |
|---|---|
| Development of individual parts of software product code | 0 |
| Homework and group projects | 1 |
| Midterm evaluation | 1 |
| Testing (written or computer based) | 1 |
| Reports | 0 |
| Essays | 0 |
| Oral polls | 0 |
| Discussions | 0 |
Typical questions for ongoing performance evaluation within this section
- How a convex set and a convex function are defined?
- What is the difference between polyhedron and polytope?
- Why does always a linear program include constraints?
Test questions for final assessment in this section
- Why does the simplex method require to be initialized with a correct basic feasible solution?
- How one can test absence of solutions to a linear program?
- How one can test unbounded solutions to a linear program?
- How can the computational complexity of an optimization algorithm can be defined?
Section 2
Section title: Nonlinear programming
Topics covered in this section
- methods for unconstrained optimization
- linear and nonlinear least-squares problems
- methods for constrained optimization
What forms of evaluation were used to test students’ performance in this section?
| Yes/No | |
|---|---|
| Development of individual parts of software product code | 0 |
| Homework and group projects | 1 |
| Midterm evaluation | 1 |
| Testing (written or computer based) | 1 |
| Reports | 0 |
| Essays | 0 |
| Oral polls | 0 |
| Discussions | 0 |
Typical questions for ongoing performance evaluation within this section
- Which are the necessary and sufficient conditions of optimality of a generic minimization/maximization problem?
- What is the goal of a descent algorithm?
- What does it mean to fit some experimental data points
Test questions for final assessment in this section
- How is it possible to compute the Lagrange multiplier of a constrained optimization problem?
- Which are the convergence conditions of the steepest descent method?
- Which are the convergence conditions of the Newton’s method?
- How can one “penalize” a constraint?