KTH /
Engineering Science
/
Mathematics
/
Optimization and Systems Theory
SF2822 Applied Nonlinear Optimization, 7.5hp, 2016/2017
Instructor and examiner
Anders Forsgren
(andersf@kth.se),
room 3533, Lindstedtsv. 25, tel 790 71 27.
Office hours: Monday 1112.
(Or by agreement.)
Exercise leader and project leader
Axel Ringh
(aringh@kth.se),
room 3734,
Lindstedtsv. 25, tel. 790 66 59.
Office hours: By agreement.
Course material

Linear and Nonlinear Optimization, second edition,
by I. Griva, S. G. Nash och A. Sofer, SIAM, 2009.
(The book can be ordered from several places. Please note that you can
become
a SIAM
member for free and obtain a discount at the SIAM bookstore.)
 Exercises in applied nonlinear optimization, 2016/2017.
Available via Canvas.
 Supplementary course material in applied nonlinear
optimization, 2016/2017.
Available via Canvas.
 Lecture notes in applied nonlinear optimization,
2016/2017. Can be downloaded from this web page, see the
schedule below. Also available via Canvas.
 GAMS, A user's guide.
May be downloaded from the GAMS web site.
 GAMS. GAMS is installed in the KTH linux computer
rooms. It may also be downloaded from the
GAMS web
site for use on a personal computer.
 Two project assignments that are handed out during the
course, March 30 and April 27 respectively.
Additional notes that may be handed out during the course are also included.
Course goals
After completed course, the student should be able to:

explain fundamental concepts of nonlinear programming;

explain how fundamental methods for nonlinear programming work;

illustrate how these methods work by solving small problems by hand
calculations;

starting from a suitably modified real problem, formulate a nonlinear
program; make a model in a modeling
language and solve the problem;

analyze the solutions of the optimization problem solved, and present
the analysis in writing as well as orally;

interact with other students when modeling and analyzing the
optimization problems.
Examination
The examination is in two parts, projects and final exam.
To pass the course, the following is required:

Pass project assignment 1, with presence at compulsory presentation
lecture on Thursday April 27, and presence at the following dicussion
session.

Pass project assignment 2, with presence at compulsory presentation
lecture on Wednesday May 17, and presence at the following dicussion
session.

Pass final exam.
Course registration
Due to the project based nature of this course, students must register
no later than March 28. Registration is made by the students online
following KTH standard procedures. PhD students are not able to
register online but register via email
to Anders Forsgren.
Project assignments
The project assignments are performed in groups, where the instructor determines the division of
groups. This division is changed between the two
assignments. Assignment 1 is carried out using the modeling language
GAMS. For project 2, there is a choice between a modeling assignment,
to be carried out using GAMS, or a method assignment, to be carried
out using Matlab. The project assignments must be carried out
during the duration of the course and completed by the above mentioned
presentation lectures. Presence at the presentation lectures is
compulsory. For passing the projects, the following requirements must
be fulfilled:

No later than the night before the presentation lecture, each group
must hand in a wellwritten report which describes the exercise and
the group's suggestion for solving the exercise. Suitable word
processor should be used. The report should be on a level suitable for
another participant in the course who is not familiar with the group's
specific problem.

When handing in the report, each student should append an individual
sheet with a brief selfassessment of his/her contribution to the project
work, quantitatively as well as qualitatively.

At the presentation lecture, all assignments will be presented and
discussed. Each student is expected to be able to present the
assignment of his/her group. In particular, each student is expected
to take part in the discussion. The presentation and discussion should
be on a level such that students having had the same assignment can
discuss, and students not having had the same assignment can
understand the issues that have arisen and how they have been solved.
 Each group should make an appointment for a discussion session
with the course leaders. There is no presentation at this session, but
these sessions are in the form of a 20 minutes question session, one
group at a time. There will be times available the days after the
presentation session. One week prior to the presentation lecture, a
list of available times for discussion sessions will be made available
at Doodle, reachable from the course home page. Each group should sign
up for a discussion session prior to the presentation lecture.
 Each participant in the course must contribute to the work of the
group. Each group must solve their task independently. Discussion
between the groups is encouraged, but each group must individually
solve the assignments. It is not allowed to use solutions
made by others in any form. If these rules are violated, disciplinary
actions in accordance with the KTH regulations will be taken.
Each project assignment is awarded a grade which is either fail or
pass with grading E, D, C, B and A. Here, the mathematical treatment
of the problem as well as the report and the oral presentation or
discussion is taken into account. Normally, the same grade is given to
all members of a group.
Final exam
The final exam consists of five exercises and gives a maximum of 50
points. At the exam, the grades F, Fx, E, D, C, B and A are awarded.
For a passing grade, normally at least 22 points are required. At the
exam, in addidion to writing material, no other material is allowed at the
exam. Normally, the grade limits are given by E (2224), D (2530), C
(3136), B (3742) and A (4350).
The grade Fx is normally given for 20 or 21 points on the final
exam. An Fx grade may be converted to an E grade by a successful
completion of two supplementary exercises, that the student must
complete independently. One exercise among the theory exercises handed
out during the course, and one exercise which is similar to one
exercise of the exam. These exercises are selected by the instructor,
individually for each student. Solutions have to be handed in to the
instructor and also explained orally within three weeks of the date of
notification of grades.
The final exam is given Thursday June 1, 8.0013.00.
Final grade
By identitying A=7, B=6, C=5, D=4, E=3, the final grade is given as
round( (grade on proj 1) + (grade on proj 2) + 2 *
(grade on final exam) ) / 4),
where the rounding is made to nearest larger integer in case of a tie.
Preliminary schedule
(Lecture notes are not yet available.)
"L" means lecture, "E" means exercise session, "P" means project sesstion.
Type  Day  Date  Time  Room  Subject


L1.  Wed  Mar 22  810  E51
 Introduction. Nonlinear programming models.
(pdf)

L2.  Thu  Mar 23  1012  Q21
 Optimality conditions for linearly constrained problems.
(pdf)

L3.  Fri  Mar 24  1315  L52
 Optimality conditions for nonlinearly constrained problems.
(pdf)

P1.  Wed  Mar 29  810  E31
 Introduction to GAMS.

P2.  Thu  Mar 30  1012 
 GAMS excercise session.

E1.  Fri  Mar 31  1315  D34
 Optimality conditions.

L4.  Wed  Apr 5  810  D34
 Unconstrained optimization.
(pdf)

L5.  Thu  Apr 6  1012  Q21
 Unconstrained optimization, cont.
(pdf)

L6.  Fri  Apr 7  1315  E51
 Equalityconstrained quadratic programming.
(pdf)

E2.  Wed  Apr 19  810  D34
 Unconstrained optimization.

E3.  Thu  Apr 20  1012  E31
 Equalityconstrained quadratic programming.

L7.  Fri  Apr 21  1315  E51
 Inequalityconstrained quadratic programming.
(pdf)

L8.  Wed  Apr 26  810  E31
 Inequalityconstrained quadratic programming, cont.
(pdf)

P3.  Thu  Apr 27  1012  D34
 Presentation of project assignment 1.

E4.  Fri  Apr 28  1315  D34
 Inequalityconstrained quadratic programming.

L9.  Wed  May 3  810  E51
 Sequential quadratic programming.
(pdf)

E5.  Thu  May 4  1012  D34
 Sequential quadratic programming.

L10.  Fri  May 5  1315  E31
 Interior methods for nonlinear programming.
(pdf)

E6.  Wed  May 10  810  D34
 Interior methods for nonlinear programming.

L11.  Thu  May 11  1012  E31
 Interior methods for nonlinear programming,
cont. Semidefinite programming.
(pdf)

L12.  Fri  May 12  1315  E31
 Semidefinite programming, cont.

P4.  Wed  May 17  810  E31
 Presentation of project assignment 2.

E7.  Thu  May 18  1012  E51
 Semidefinite programming.

E8.  Fri  May 19  1315  D34
 Selected topics.

Overview of course contents
 Unconstrained optimization
Fundamental theory, in particular optimality conditions.
Linesearch algorithms, steepest descent, Newton's method.
Conjugate directions and the conjugate gradient method.
QuasiNewton methods.
(Chapters 11, 12.112.3 and 13.113.2 in Griva, Nash and Sofer.)
 Constrained nonlinear optimization
Fundamental theory, optimality conditions, Lagrange multipliers and sensitivity analysis.
Quadratic programming.
Primal methods, in particular activeset methods.
Penalty and barrier methods, in particular primaldual interior methods.
Dulal methods, local duality, separable problems.
Lagrange methods, in particular sequential quadratic programming.
(Chapters 3, 14.114.7, 14.8.1, 15.115.5, 16.116.3 and 16.7 in
Griva, Nash and Sofer.)
 Semidefinite programming
Fundamental theory.
(Chapter 16.8 in Griva, Nash and Sofer. Separate article in the
supplementary course material. Fundamental concepts only.)
Welcome to the course!
Course web page:
http://www.math.kth.se/optsyst/grundutbildning/kurser/SF2822/.
