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SF2822 Applied Nonlinear Optimization, 7.5hp, 2018/2019

Instructor and examiner

Exercise leader and project leader

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, 2018/2019. Available via Canvas.
• Supplementary course material in applied nonlinear optimization, 2018/2019. Available via Canvas.
• Lecture notes in applied nonlinear optimization, 2018/2019. Can be downloaded from this web page, see the schedule below. Also available via Canvas.
• GAMS, A user's guide. Available at 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, April 5 and April 25 respectively.

Additional notes that may be handed out during the course are also included.

Course goals

• 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

• Pass project assignment 1, with presence at compulsory presentation lecture on Thursday April 25, and presence at the following dicussion session.
• Pass project assignment 2, with presence at compulsory presentation lecture on Friday May 10, and presence at the following dicussion session.
• Pass final exam. Please note that advance application for participation in examinations is compulsory according to KTH's rules. This is done via "My Pages" for master students and via a particular form for PhD students. More information can be found here.

Course registration

Project assignments

• No later than the night before the presentation lecture, each group must hand in a well-written 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 self-assessment 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 15 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 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 Friday May 31, 8.00-13.00.

Final grade

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

"L" means lecture, "E" means exercise session, "P" means project sesstion.

Type	Day	Date	Time	Room	Subject
L1.	Mon	Mar 18	15-17	U31	Introduction. Nonlinear programming models. (pdf)
L2.	Thu	Mar 21	10-12	U31	Optimality conditions for linearly constrained problems. (pdf)
L3.	Fri	Mar 22	13-15	K51	Optimality conditions for nonlinearly constrained problems. (pdf)
E1.	Mon	Mar 25	15-17	U21	Optimality conditions.
L4.	Thu	Mar 28	10-12	U31	Unconstrained optimization. (pdf)
L5.	Fri	Mar 29	13-15	U21	Unconstrained optimization, cont. (pdf)
E2.	Mon	Apr 1	15-17	Q21	Unconstrained optimization.
P1.	Wed	Apr 3	8-10	Q21	Introduction to GAMS.
P2.	Fri	Apr 5	10-12	Gul	GAMS excercise session.
L6.	Mon	Apr 8	15-17	Q21	Equality-constrained quadratic programming. (pdf)
E3.	Tue	Apr 9	10-12	U41	Equality-constrained quadratic programming.
L7.	Wed	Apr 10	8-10	Q21	Inequality-constrained quadratic programming. (pdf)
L8.	Thu	Apr 11	10-12	U31	Inequality-constrained quadratic programming, cont. (pdf)
E4.	Fri	Apr 12	13-15	K51	Inequality-constrained quadratic programming.
L9.	Wed	Apr 24	8-10	U21	Sequential quadratic programming. (pdf)
P3.	Thu	Apr 25	10-12	U31	Presentation of project assignment 1.
E5.	Fri	Apr 26	13-15	U21	Sequential quadratic programming.
L10.	Thu	May 2	10-12	M33	Sequential quadratic programming, cont. Interior methods for nonlinear programming. (pdf)
L11.	Fri	May 3	13-15	U31	Interior methods for nonlinear programming, cont. (pdf)
E6.	Thu	May 9	10-12	U31	Interior methods for nonlinear programming.
P4.	Fri	May 10	13-15	U21	Presentation of project assignment 2.
L12.	Mon	May 13	15-17	K51	Semidefinite programming.
E7.	Thu	May 16	10-12	U31	Semidefinite programming.
E8.	Fri	May 17	13-15	U21	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.
  Quasi-Newton methods.
  (Chapters 11, 12.1-12.3 and 13.1-13.2 in Griva, Nash and Sofer.)
• Constrained nonlinear optimization
  Fundamental theory, optimality conditions, Lagrange multipliers and sensitivity analysis.
  Quadratic programming.
  Primal methods, in particular active-set methods.
  Penalty and barrier methods, in particular primal-dual interior methods.
  Dulal methods, local duality, separable problems.
  Lagrange methods, in particular sequential quadratic programming.
  (Chapters 3, 14.1-14.7, 14.8.1, 15.1-15.5, 16.1-16.3 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!