Print syllabusNonlinear optimization
General data
| Course ID: | 1000-135OPN |
| Erasmus code / ISCED: |
11.913
|
| 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
|
| 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 2023/24" (past)
| Time span: | 2023-10-01 - 2024-01-28 |
 
MO TU W TH WYK
CW
FR |
| Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
| Coordinators: | Agnieszka Wiszniewska-Matyszkiel | |
| Group instructors: | Agnieszka Wiszniewska-Matyszkiel | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Classes in period "Winter semester 2024/25" (future)
| Time span: | 2024-10-01 - 2025-01-26 |
MO TU W TH FR |
| Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
| Coordinators: | Agnieszka Wiszniewska-Matyszkiel | |
| Group instructors: | Agnieszka Wiszniewska-Matyszkiel | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Copyright by University of Warsaw.
