The course is as an introduction to computational optimization. We will cover some theory for linear and nonlinear optimization, discuss classes of important applications, and introduce computational algorithms. The text book is Linear and Nonlinear Programming, by Stephen Nash and Ariela Sofer.
The time will be divided about equally between linear programming, unconstrained nonlinear optimization, and nonlinear programming (that is, nonlinear optimization with constrains). We will define Linear Programs (LPs) and describe the simplex method for the solution of LPs. More general types of optimization problems are called Nonlinear Programs (NLPs). We will first discuss iterative methods used to find local optima for unconstrained NLPs. Finally, we will discuss nonlinear optimization problems with constraints, characterizations of solutions to such problems, and give a short orientation of numerical methods for solving NLPs.
There are 18 lectures, 3 computational assignments, and one written final examination. A passing grade in the final exam and a passing grade in each of the computational assignments are necessary to pass the course. The final exam is on Wednesday October 25, 2006. The assignments will be handed out during the course. The subjects are: linear programming, nonlinear least-squares optimization, and nonlinear programming. Detailed descriptions of the tasks will be provided later. The following applies to the assignments:
The course will be in Swedish if no foreign students take the course, otherwise in English. A preliminary schedule of the course is found in the table below. It is likely that some delays and changes in content will occur. Lecture notes will mainly be given on the blackboard, with some additional material provided on viewgraphs. Pdf files with the viewgraph material will be put on the home page continuously throughout the course. Exercises will be taken from the book, from old exams, or from material handed out at the lectures.
|Lect.||Topic||Sections in the book||Day||Time||Room|
|1||Introduction||1 , 2 (just skim it)||Aug. 29||8-10||P1111|
|2||Linear Programming||4||Aug. 30||10-12||P1111|
|3||Linear Programming||4||Sep. 4||13-15||P2247|
|4||Linear Programming||5.1-5.2||Sep. 6||10-12||P1111|
|5||Linear Programming||6.1-6.2, 6.4||Sep. 7||8-10||P1111|
|7||Unconstr. nonlin. opt., intro||10.1-10.2, 2.4-2.5||Sep. 15||10-12||Häggsalen|
|8||Unconstr. nonlin. opt||10.3-10.5||Sep. 19||8-10||P1111|
|9||Unconstr. nonlin. opt||11.1-11.2||Sep. 21||10-12||P2146|
|10||Unconstr. nonlin. opt||11.3, 11.4||Sep. 22||13-15||P2247|
|11||Nonlinear Least Squares||13.1, 13.2||Sep. 25||8-10||P2247|
|13||Nonlinear Programming||14.2-14.3||Oct. 2||10-12||P2347|
|14||Nonlinear Programming||14.4-14.6||Oct. 6||13-15||P1311|
|15||Nonlinear Programming||15-16 (orientation)||Oct. 9||15-17||P1111|
|18||Examples from old written exams||old examinations||Oct. 18||13-15||P2446|
Lecturer is Martin Berggren. Office 2451, ph. 471 2964, .
The course homepage is at http://www.it.uu.se/edu/course/homepage/opt1