ELEC-E5424 - Convex optimization D, Lecture, 6.9.2023-14.12.2023
This course space end date is set to 14.12.2023 Search Courses: ELEC-E5424
Översikt
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Schedule
Lectures (Wed. 9.15-11:00)
Exercises (Thu. 12:15-14:00)
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 (9:00-11:00): T3
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
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.
• 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.
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
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Some concepts from linear algebra that are heavily used in the textbook for the course and in general in convex optimization.
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Convex Sets Fil 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
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convex functions, epigraph (simple examples, elementary properties)
more examples, more properties
Jensen's inequality
quasiconvex, quasiconcave functions
log-convex and log-concave functions
K-convexity
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abstract form problem
standard form problem
convex optimization problem
standard form with generalized inequalities
mulitcriterion optimization
restriction and relaxation
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linear programming (examples and applications)
linear fractional programming
quadratic optimization problems
(quadratically constrained) quadratic programming
examples and applications
Semidefinite programming
applications
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Duality Fil 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
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terminology
general descent method
line search types
gradient method
steepest descent method
Newton's method
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brief history of SUMT & IP methods
logarithmic barrier function
central path
basic SUMT
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Assignment 1 Inlämningsuppgift
Convex Sets
Due to October 8, 2023
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Assignment 2 Inlämningsuppgift
Convex Functions
Due to October 29, 2023.
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Solutions to Assignment 2 Fil PDF
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Assignment 3 Inlämningsuppgift
Convex Problems
Due to November 12, 2023.
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Assignment 4 Inlämningsuppgift
Duality, Applications, and Algorithms
Last Assignment!
Due to November 26, 2023.