ELECE5424  Convex optimization D, Lecture, 6.9.202314.12.2023
This course space end date is set to 14.12.2023 Search Courses: ELECE5424
Topic outline

Schedule
Lectures (Wed. 9.1511:00)
Exercises (Thu. 12:1514:00)
13.9
Lect. 1: T3 Computer Science build.
14.9
Lect. 2/Exer.: TU7 Maarintie 8
20.9
Lect. 3: T3 Computer Science build.
21.9
Lect. 4/Exer.: TU7 Maarintie 8
27.9
Lect. 5: T3 Computer Science build.
28.9
Lect. 6/Exer.: TU7 Maarintie 8
4.10
Lect. 7: T3 Computer Science build.
11.10
Lect. 8: T3 Computer Science build.
12.10
Exer. 1: TU7 Maarintie 8
Exam week (no teaching)
Exam week (no teaching)
25.10
Lect. 9: T3 Computer Science build.
26.10
Lect. 10/Exer.: TU7 Maarintie 8
1.11
Lect. 11: T3 Computer Science buil.
2.11
Exer. 2: TU7 Maarintie 8
8.11
Lect. 12: T3 Computer Science buil.
15.11
Lect. 13: T3 Computer Science buil.
16.11
Exer. 3: TU7 Maarintie 8
22.11
Lect. 14: T3 Computer Science buil.
29.11
Exer. 4: T3 Computer Science build.
Preparation week
Preparation week
13.12
Exam (9:0011:00): T3
Textbook and Optional References
• Stephen Boyd; Lieven Vandenberghe, Convex Optimization (Textbook!)
• BenTal 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
Course Requirements and Grading
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.
Grading:
Homeworks: 60%. Exam: 40%. These weights are approximate. We reserve the right to change them later. Can be also discussed.
Description
Concentrates on recognizing and solving (using standard packages) convex optimization problems that arise in practice!
• Convex sets, functions, and optimization problems.
• Leastsquares, 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 interiorpoint methods for constrained optimization.
• Applications.
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


Convex Sets File PDF
subspace, afiine set, convex set, convex cone (simple examples and properties)
combination and hulls
ellipsoids, polyhedra, norm balls
affine and projective transformations
separating hyperplanes
generalized inequalities


Duality File PDF
Lagrange dual function
Lagrange dual problem
strong duality and Slater's condition
KKT optimality conditions
sensitivity analysis
duality in generalized inequalities notation
theorem of alternatives

Assignment 1
Convex Sets
Due to October 8, 2023

Assignment 2
Convex Functions
Due to October 29, 2023.

Solutions to Assignment 2 File PDF

Assignment 3
Convex Problems
Due to November 12, 2023.

Assignment 4
Duality, Applications, and Algorithms
Last Assignment!
Due to November 26, 2023.