MSc: Optimization

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 constraints. The course takes a unified view of optimization and covers the main areas of application and the main optimization algorithms. It covers linear 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%)