Convex Optimization
Data is displayed for academic year: 2023./2024.
Lecturers
Associate Lecturers
Course Description
The course concentrates on recognizing and solving convex optimization problems that arise in applications. Basics of linear programming. Convex sets, convex functions, and convex optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, linear matrix inequalities, semidefinite programming. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance.
Study Programmes
University graduate
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Learning Outcomes
- define a linear programming problem and identify the associated dual problem
- explain the idea of the simplex method
- breakdown the steps of the primary-dual inner-point method for linear problems
- identify convex optimization problem
- analyze Karush-Kuhn-Tucker optimality conditions
- create a dual problem and analyze the sensitivity of the optimum to the perturbations of the constraints
- recognize the problem of semidefinite programming
- apply and modify appropriate numerical conditional optimization methods
Forms of Teaching
Lectures
3 hours of lectures per week
Grading Method
Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|
Type | Threshold | Percent of Grade | Threshold | Percent of Grade | ||
Class participation | 0 % | 5 % | 0 % | 5 % | ||
Mid Term Exam: Written | 0 % | 20 % | 0 % | |||
Final Exam: Written | 0 % | 25 % | ||||
Final Exam: Oral | 50 % | |||||
Exam: Written | 0 % | 45 % | ||||
Exam: Oral | 50 % |
Week by Week Schedule
- Convexity; Polyhedra, convex hulls, polytopes
- The simplex method
- Duality and sensitivity, Primal-dual interior-point method for linear programming
- Convex sets and convex functions
- Convex optimization problems
- Quadratic problems (box-constrained, equality constrained, inequality constrained)
- Tangent cone and constraint qualifications
- Midterm exam
- Karush-Kuhn-Tucker optimality conditions
- Duality; The Lagrange function; Perturbation and sensitivity analysis
- Linear matrix inequalities; Eigenvalue problems
- Semidefinite programming
- Active set methods for convex quadratic problems
- Interior point methods for convex optimization problems
- Final exam
Literature
For students
General
ID 222633
Winter semester
5 ECTS
L1 English Level
L1 e-Learning
45 Lectures
0 Seminar
0 Exercises
0 Laboratory exercises
0 Project laboratory
Grading System
87.5 Excellent
75 Very Good
62.5 Good
50 Sufficient