Loading
2006-02-07: Finally, we have put together a home page for the course mentioned below. Please contact me if you are interested in the course!
During the later half of the spring semester, there will be a graduate-level course organized by FMB
(the Graduate School in Mathematics and Computing) that may be of interest to some of you (although it is primarily directed towards Ph. D. students). Note that the course is not listed on FMB's homepage yet. The course consist of three "modules": (i) Numerical Optimization. This part will be given by professor Anders Forsgren at KTH, Stockholm and will be cover similar issues as in the present course, but on a somewhat more advanced level.(ii) Optimal control of ordinary, partial, and stochastic differential equations with applications for instance in financial mathematics. This part will be given by professor Anders Szepessy at KTH, Stockholm. (iii) Inverse problem for partial differential equations, shape, and topology optimization with applications for instance in heat conduction and structural optimization. I will lecture on the last part. Contact me
for more information. Later during the fall I will set up a homepage with more information.
2006-01-22: The result of the 2006-01-12 exam is now available at the password-protected page. The exams can be picked up at the IT office.
2005-11-11: The result of the 2005-10-25 exam is now available at the password-protected page. The exams can be picked up at the IT office.
2005-11-10: The 2005-10-25 exam with solutions is now available at the page with old exams. I hope to be able to report the results on Friday, Nov 11.
2005-10-18: Note that the absolute deadline for this year's assignment is November 4 and nothing else. (Previously I erroneously said October 31 below!)I have switched the IN and OUT boxes for the assignments due to key problems.
2005-10-05: Regarding Assignment 2. Some of you, marked with C? in the table on the password-protected page, got an immediate return for corrections due to insuffient reporting. Please follow the instructions. (The reports are in the out box on the second florr in house 2.). Please remember to attached the old report when you resubmit a corrected report. (I cannot always remember exactly what should be corrected.) Åsa B and Sofia E, I want to see your old report for Assignment 1!
2005-09-30: I have put all the graded reports from Assignment 1 in box 14 (marked Optimization) on the second floor in house 2.
2005-09-29: I have now graded Assignment 1. Unfortunately, there is quite a few of you that need to hand in corrections. The most common error is the formulation of the dual problem in part 1. Remember that each linear program has a unique dual. I say that again: each linear program has a unique dual. If you rewrite the primal problem to an equivalent problem (by multiplying the constraints by minus 1 for instance) and calculate the dual of the rewrited LP, you get the dual of the rewritten LP and not necessarily the dual of the original problem. The sign of the dual varibles may change, for instance, if you rewrite the primal problem. Why does this mattter? It is because the sign of the dual variables is important: it gives sensitivity information of the right-hand side to corresponding primal problem.
When you hand in correction, remember to attach also the old version so I can see what changes you have made.
2005-09-21: Tomorrow is the deadline to hand in Assignment 1 to obtain 1/2 bonus points on the final exam (the bonus will be given if the solution is correct or almost correct). You can hand in the assignment to me at the lecture, in my office, or leave it in the box marked Opt 1 on the second floor of house 2.
I (Martin) will add messages here throughout the course.
Here, you can download pdf-files with the viewgraphs that are shown during lectures. These are either reviews from previous lecture or material to complement the lecture notes given on the black board.
Lecture 1: Examples of Linear Programs
Lecture 2: Definition of basic solutions. The fundamental theorem of linear programming.
Lecture 3: Review: The geometry of feasible sets.
Lecture 4: Review: The simplex method.
Lecture 6: Review: Duality.
Lecture 7: Review: Convexity. Example of an unconstrained optimization problem.
Lecture 8: Review: basic notions in nonlinear programming.
Lecture 9: Review: Newton's method for minimization.
Lecture 10: Review: Steepest descent and quasi-Newton.
Lecture 12: Handout: Automating/avoiding derivative calculations
Lecture 13: Handout: Geometric motivaition of the KKT conditions
Lecture 14: Review: The KKT conditions.
Lecture 15: Review: Quadratic Programs. An example of a log barrier.
Lecture 16: Review: Algorithms for Nonlinear Programming.
Suggested problems from the textbook.
Absolute deadline for this years assignments: November 4
You can view the status of the assignments here. You will need to supply a user name and password: First choose the login directory Anonymous from the drop-down menu (välj inloggningskatalog Anonym från rullgardinsmenyn), then use the login name opt1 plus the password that I told you in class. Email me for it if you don't remember it. Pick up corrected assignments in the outbox on the second floor in house 2.
Assignment1: Linear programming. 0.5 bonus point on final exam if correct solution handed in September 22 at the latest.
Assignment2: An inverse problem for heat condation. 0.5 bonus point on final exam if correct solution handed in October 5 at the latest. You will need the Matlab m-files temperatures.m and param.m.
Assignment3: Portfolio optimization 0.5 bonus point on final exam if correct solution handed in October 20 at the latest.
You can find a collection of old exams with solutions here.
Note that the course content has changed somewhat from previous years. This year's syllabus does not include global optimization (typically question 6 on the old exams), nor have we covered network problems this year. Instead there will be at least one problem on nonlinear optimization with constraints on this year's exam.
| Link types on this page: | External link |
Email address |
PDF document |