Information
Neptun ID, timetable, classroom
IMEN102E/G,Monday 10-13
Description
Requirements
Attendance of the lectures is highly recommended. Attendance is registered. In-class performance is assessed and its results form part of the end-term grade. The final score (%) of the course is constructed as follows: 20% lecture and seminar attendance, 30% in-class test 50% homework/project presentation (last two lectures of the semester).
Grades (based on percentages)
- 80-100: 5 (excellent)
- 70-79: 4 (good)
- 60-69: 3 (medium)
- 50-59: 2 (satisfactory)
- 0-49: 1 (fail)
Online available material
see Coospace
Syllabus
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Lecture 1
Motivational examples and introduction to nonlinear programming, examples, basic definitions.
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Lecture 2
Unconstrained optimization: Gradient, Hessian, definitness of matrices and its relation to optima, Weierstrass-theorem.
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Lecture 3
Unconstrained optimization: 1st and 2nd order necessary condition for optimality; some geometry; the general line search method. Convexity and minimization.
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Lecture 4
Newton’s method for unconstrained optimization, convergence rate, excercises.
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Lecture 5
Quadratic optimization problem and examples.
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Lecture 6
Steepest descent method for unconstrained optimization. Conjugate gradient method.
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Lecture 7
Constrained optimization I: Lagrange dual function, duality theorems, KKT theorem.
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Lecture 8
Constrained optimization II: more on dulaity
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Lecture 9
Constrained optimization III: penalty and barrier methods
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Lecture 10
More on nonlienar programming models of real-life problems
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Lecture 11
More on nonlienar programming in machine learning
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Lecture 12
Project presentations, closing the semester.