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SF2822 Applied Nonlinear Optimization 7.5 credits

Tillämpad ickelinjär optimering

The course gives deepened and broadened theoretical and methodological knowledge in nonlinear programming. Some subjects dealt with in the course are: Sequential-quadratic-programming methods, primal-dual interior methods, semidefinite programming, convexity, convex relaxations.

The course also gives training in modeling and solving practical problems, and to present the results in talking as well as in writing.

  • Educational level

    Second cycle

  • Academic level (A-D)

    D

  • Subject area

    Mathematics

  • Grade scale

    A, B, C, D, E, FX, F

Course offerings

Spring 13 for programme students

Spring 14 for programme students

  • Periods

    Spring 14 P4 (7.5 credits)

  • Application code

    60276

  • Start date

    2014 week: 13

  • End date

    2014 week: 23

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Number of lectures

  • Number of exercises

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

  • Course responsible

    Anders Forsgren <andersf@kth.se>

  • Teacher

    Anders Forsgren <andersf@kth.se>
    Tove Odland <odland@kth.se>

  • Target group

    SwB Computational Science and Engineering

Spring 14 for programme students

Learning outcomes

To deepen and broaden the student's theoretical and methodological knowledge in nonlinear programming.

To give training in the art of modeling and solving practical problems, and in presenting the results.

Course main content

Theory and methods:

Newton methods, Quasi-Newton methods, and conjugate-gradient methods for unconstrained optimization. Optimality conditions, quadratic programming, SQP methods, and primal-dual interior methods for nonlinearly constrained optimization. Semidefinite programming and interior methods. Convexity and convex relaxations.

Projects:

This part of the course consists of modeling practical optimization problems and using available optimization software to solve them. The projects are carried out in small groups. An important aspect of the course is cooperation within the group as well as presentations in talking and in writing.

Eligibility

In general:

150 university credits (hp) including 28 hp in Mathematics,  6 hp in Mathematical Statistics and 6 hp in Optimization. Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis, optimization. A passed second course in numerical analysis is an advantage.

Prerequisites

The prerequisites is a Swedish or foreign degree equivalent to Bachelor of Science of 180 ECTS credits, with at least 45 ECTS credits in mathematics. The students should have documented knowledge corresponding to basic university courses in analysis, linear algebra, numerical analysis, differential equations and transforms, mathematical statistics, and optimization.

Literature

To be announced at the beginning of the course. Preliminary literature:

Linear and Nonlinear Programming by S.G.Nash och A.Sofer, McGraw-Hill, and some material from the department.

Examination

  • PRO1 - Project, 1.5 credits, grade scale: A, B, C, D, E, FX, F
  • PRO2 - Project, 1.5 credits, grade scale: A, B, C, D, E, FX, F
  • TEN1 - Examination, 4.5 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

A written exam (TEN1; 4,5 hp).
Projects (PRO1; 3 hp).

Offered by

SCI/Mathematics

Examiner

Anders Forsgren <andersf@kth.se>

Version

Course plan valid from: Spring 11.
Examination information valid from: Autumn 07.