Syllabus

LEARNING OUTCOMES

Students will be introduced to and trained to use the tools to recognize convex optimization problems that arise in engineering, scince, economics. They will be introduced to the basic theory of such problems, concentrating on results that are useful in computation and engineering and computer science practice. The basic numerical optimization algorithms will be also practiced. Students will also be introduced to basic formats of convex optimization problems that are needed as an input form for convex optimization solvers, such as CVX, and will learn how to use convex optimization tools and existing solvers in their research.

Credits: 5

Schedule: 04.09.2024 - 04.12.2024

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Sergiy Vorobyov

Contact information for the course (applies in this implementation):

Teacher is Prof. Sergiy A. Vorobyov: Dr. Sergiy Vorobyov (aalto.fi)

TAs are: Kiarash H. Irani: kiarash.hassasirani@aalto.fi

and        Tingting Zhang: tingting.zhang@aalto.fi

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs. Semidefinite programming. Solvers.

• applies in this implementation

  Concentrates on recognizing and solving (using standard packages) convex optimization problems that arise in practice!

  •        Convex sets, functions, and optimization problems.

  •        Least-squares, linear and quadratic programs.

  •        Semidefinite programming (SDP).

  •        Minimax, extremal volume, and other problems with geometric interpretation.

  •        Optimality conditions, duality theory, theorem of alternatives.

  •        Introduction to unconstrained optimization algorithms.

  •        Introduction to interior-point methods for constrained optimization.

  •        Applications.

  
  

Assessment Methods and Criteria

• valid for whole curriculum period:

  Lectures (excercise problems are solved in the lectures), assignments, exam.

• applies in this implementation

  Requirements:

  •        4 homework assignments. Homeworks will normally be assigned on Wedndsdays and will be due in 2 weeks.

  •        Final Exam. The format will be decided depending on the situation.

  Grading: 

  Homeworks: 60%. Exam: 40%. These weights are approximate. We reserve the right to change them later. Can be also discussed.

  
  

Workload

• valid for whole curriculum period:

  Lectures (excercise problems are solved in the lectures) and exam, assignments and independent studying

• applies in this implementation

  In class work: 

  14 Lectures, but lectures will contain not only theory, but also problem solving (exercises). 

  4 Exercises. Exercises are for solving some homework problems and some additional interesting problems. 

  For distribution of hours between the in class work and home work see SISU.
  

DETAILS

Study Material

• applies in this implementation

  Textbook and Optional References

  •        Stephen Boyd; Lieven Vandenberghe, Convex Optimization (Textbook!)

  •        Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications

  •        Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course

  •        J. Gallier and J. Quaintance, Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Engineering

  
  

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language: English

  Teaching Period: 2024-2025 Autumn I - II
  2025-2026 Autumn I - II

• applies in this implementation

  Course Objectives

  •        to give the tools and training to recognize convex optimization problems that arise in electrical engineering and computer science

  •        to present the basic theory of such problems, concentrating on results that are useful in computations

  •        to give a thorough understanding of how such problems are solved, and some experience in solving them

  •        to give the background required to use the standard methods and software packages (CVX toolbox) in your own research work

  •        to give a number of examples of successful application of convex optimization techniques for solving problem in applied mathematics, computer science, statistics, electrical engineering, and science and engineering in general

  
  

Details on the schedule

• applies in this implementation

  Schedule

  	Lectures (Wed. 9.15-11:00)		Exercises (Thu. 12:15-14:00)
  4.9	Lect. 1: Meitner 1571, Kide
  11.9	Lect. 2: Meitner 1571, Kide	12.9	Lect. 3: Meitner 1571, Kide
  18.9	Lect. 4: Meitner 1571, Kide
  25.9	Lect. 5: Meitner 1571, Kide	26.9	Lect. 6: Meitner 1571, Kide
  2.10	Lect. 7: Meitner 1571, Kide	3.10	Exer. 1: Meitner 1571, Kide
  9.10	Lect. 8: Meitner 1571, Kide	10.10	Lect. 9: Meitner 1571, Kide
  	Exam week (no teaching)		Exam week (no teaching)
  23.10	Lect. 10: Meitner 1571, Kide	24.10	Exer. 2: Meitner 1571, Kide
  30.10	Lect. 11: Meitner 1571, Kide
  6.11	Lect. 12: Meitner 1571, Kide	7.11	Lect. 13: Meitner 1571, Kide
  13.11	Exer. 3: Meitner 1571, Kide
  20.11	Lect. 14: Meitner 1571, Kide
  27.11	Exer. 4: Meitner 1571, Kide
  4.12	Exam (9:15-10:45): D-Sali Y122, Undergraduate Centre

  
  
  

  
  

Description