Optimization

Course name: Optimization
Course number: XYZ
Knowledge area: Data Science

Administrative details

Faculty: Computer Science and Engineering
Year of instruction: 3rd year of BS
Semester of instruction: 2nd semester
No. of Credits: 5 ECTS
Total workload on average: 180 hours overall
Class lecture hours: 2 per week.
Class tutorial hours: 2 per week.
Lab hours: 2 per week.
Individual lab hours: 0.
Frequency: weekly throughout the semester.
Grading mode: letters: A, B, C, D.

Prerequisites

Familiarity with multivariate calculus, elementary real analysis, and linear algebra.

Multivariate calculus
Linear Algebra
Probability and Statistics

Course outline

This course studies fundamental concepts of optimization, which is the problem of making decisions to maximize or minimize an objective in the presence of complicating constraints. The course takes a unified view of optimization and covers the main areas of application and the main optimization algorithms. It covers the following main topics: Linear optimization, Network flows, Discrete optimization, Dynamic optimization, and Nonlinear optimization.

Expected learning outcomes

After this course, students will be able to:

be able to formulate problems in their fields of research as optimization problems
be able to transform an optimization problem into its standard form
understand how to assess and check the feasiblity and optimality of a particular solution to a general constrained optimization problem
be able to use the optimality conditions to search for a local or global solution from a starting point.
understand the computational details behind the numerical methods discussed in class, when they apply, and what their convergence rates are.
be able to implement the numerical methods discussed in class and verify their theoretical properties in practice.
be able to apply the learned techniques and analysis tools to problems arising in their own research.

Expected acquired core competences

Numerical analysis
Numerical optimization

Detailed topics covered in the course

Linear Optimization
Simplex Methods
Duality Theory
Sensitivity Analysis
Network Flows
Branch and Bound and Cutting planes
Lagrangean Methods
Dynamic Programming
Nonlinear Optimization
Optimality conditions and Gradient methods
Markov Chains and Markov Decision Processes
Stochastic Optimization

Textbook

Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization
J. Nocedal and S. Wright. Numerical Optimization

Reference material

NA

Required computer resources

NA

Evaluation

Quizzes (20%)
Labs (10%)
Midterm Exam (25%)
Final Exam (25%)
Class and lab participation (10%)

MSc: Optimization

Contents