ELEC-E5424 - Convex optimization D, Lecture, 6.9.2023-14.12.2023

Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

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:

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):

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
• 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

Description

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 Wendsdays and will be due in 2 weeks.

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

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

Important to stress that what is evaluated is not only correctness, but also the reasoning for solving problems since there can be multiple solutions that are correct!!!

• valid for whole curriculum period:

Lectures (excercise problems are solved in the lectures) and exam approximately 30 h, assignments and independent studying approximately 103 h, total 133 h

• applies in this implementation

The work load consists of hours for lectures and some exercises and the hours of individual work on the assignments and lecture materials. Independent studying accumulates to significantly more hours that we stay in class. Thus, use your time efficiently: addend every class and ask as many questions as you have.

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

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

Substitutes for Courses
• valid for whole curriculum period:

Prerequisites
• valid for whole curriculum period:

FURTHER INFORMATION

Further Information
• valid for whole curriculum period:

Teaching Language : English

Teaching Period : 2022-2023 Autumn I - II
2023-2024 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

Can be found in SISU, but lectures are every week on Wednesdays from 9:15 to 11:00 in T3 (Computer Science Building).