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Nonlinear optimization

General data

Course ID:	1000-135OPN
Erasmus code / ISCED:	11.913 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0619) Information and Communication Technologies (ICTs), not elsewhere classified The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Nonlinear optimization
Name in Polish:	Optymalizacja nieliniowa
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective courses
Prerequisites (description):	(in Polish) analiza matematyczna wielowymiarowa - podstawy
Short description:	Finding minima and maxima of functions on sets given by systems of nonlinear equations and inequalities. Lagrange multipliers, Kuhn-Tucker conditions, dual techniques. Special attention is given to convex optimisation.
Full description:	Introduction to non-linear optimisation problems. Examples of practical models. Convex sets. Separating and supporting hyperplanes. Convex functions. Once and twice differentiable convex functions. Gradient and sub-gradient. Quasi- and pseudo-convex functions. Sublevel sets. Minimas. Feasible set. Feasible directions. Necessary and sufficient conditions for optimality. Lagrange function. Fritz-John necessary condition. Kuhn-Tucker necessary and sufficient conditions. Regularity conditions. Equlibrium conditions. Dual problem and dual theorem. Saddle points of the Lagrange function, their relation to duality and Kuhn-Tucker equation. Linear complementary problem, Lemke's method, applications to quadratic programming. Solutions to quadratic programming problems. Methods of solution of nonlinear programming problems. Unconditional minimisation of one- and multi-dimensional functions. Examples of gradient methods, conjugate gradient methods and Newton-type methods. Conditional optimisation: method of feasible directions, penalty and barrier functions, random methods.
Bibliography:	A.L. Peresini, F.E. Sullivan, J.J Uhl, The mathematics of nonlinear programming. Undergraduate Texts in Mathematics. Springer-Verlag, 1988 M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming; Theory and Algorithms. John Wiley and Sons, 1993.
Learning outcomes:	(in Polish) Wiedza i umiejętności: 1. wie na czym polega zadanie optymalizacji nieliniowej w n wymiarach; 2. zna podstawowe własności zbiorów wypukłych, zna twierdzenie o hiperpłaszczyźnie rozdzielającej i podpierającej; 3. zna podstawowe własności funkcji wypukłych, zna pojęcie gradientu i subgradientu funkcji wypukłej, wie co to są funkcje quasi- i pseudowypukłe; 4. umie znajdować ekstrema funkcji wielu zmiennych, wie co to jest funkcja Lagrange'a oraz jak ją wykorzystujemy przy znajdowaniu ekstremów funkcji wielu zmiennych;
Assessment methods and assessment criteria:	(in Polish) egzamin końcowy

Classes in period "Winter semester 2024/25" (past)

Time span:	2024-10-01 - 2025-01-26	Selected timetable range: weekly course term Go to timetable MO TU W TH WYK CW FR
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Agnieszka Wiszniewska-Matyszkiel
Group instructors:	Agnieszka Wiszniewska-Matyszkiel
Students list:	(inaccessible to you)
Credit:	Examination

Classes in period "Winter semester 2025/26" (future)

Time span:	2025-10-01 - 2026-01-25	Selected timetable range: weekly course term Go to timetable MO WYK CW TU W TH FR
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Błażej Miasojedow
Group instructors:	Błażej Miasojedow
Students list:	(inaccessible to you)
Credit:	Course - Examination Lecture - Examination

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