Material: this course is an introduction to optimization techniques. In a nutshell, we will look for extrema of functions under various conditions and constraints. The course will cover the followings: optimality conditions for unconstrained and constrained optimization problems (including Lagrange and KKT multipliers), algorithms to find minima of functions (including Newton's and other gradient type methods in 1D and in several dimensions) and linear programming (basic solutions, simplex method, duality theory). There will be an accent on the theoretical understanding of the phenomena. Thus, the course is not only computation oriented. For instance, we will prove the convergence of the considered algorithms.
Instructor: Alpár R. Mészáros, MS 5230 (check the e-mail address on my webpage or on CCLE)
Schedule of classes: MWF - 8-8h50AM (Lec 1); 11-11h50AM (Lec 2)
Office hours: M-W, 9h00-10h30AM
Location: MS 6229 (Lec 1), MS 5137 (Lec 2)
TAs: Jialin Liu (Lec 1), MS 2943; Yehonatan Sella (Lec 2), MS 3965 (check e-mail addresses on CCLE)
Discussion: Lec 1: Tuesday, 8-8h50AM (same room as for the lecture); Lec 2: Thursday, 11-11h50AM (same room as for the lecture)
TAs' office hours: TBA
Textbook: E. K.P. Chong and S. Zak, An Introduction to Optimization, Wiley, 4th Edition, (2013).
Requisites: multivariable calculus and tools from linear algebra will be used continuously. Notions such as gradient, Hessian matrix, Taylor expansion in multiple variables, matrix operations, eigenvalues, eigenspaces, etc. will be recalled, but are supposed to be known material. Thus courses as Math 115A and Math 32A are recommended to follow the lectures.
Homework problems will be assigned weekly (i.e. 10 sets) and collected at the beginning of the Friday lecture (if Friday is a holiday the collection date is next Monday at the beginning of the lecture). The purpose of the homework exercises is to deepen the notions and the concepts learned during the courses. A second purpose is to gain experience with computation techniques. Please note that late- or no homework papers will be graded as zero, but the two lowest homework scores will be dropped in the computation of your final grade (see 'Grading' section below). The homework sheets will appear on this webpage, approximately 1 week before their deadline. There is a possibility to work in groups on the homework problems. In this case, everybody from the group has to submit his/her own homework paper and should write the names of the other students from his/her group on the top of the papers.
Exams: there will be one midterm (see the precise date below) and a written final exam at the end. No make-up exams will be provided, a missed exam is graded as zero. You must take the final in order to pass the class!
Grading: the final score is calculated as follows. I will chose the scheme which gives you higher final score:
10% HG + 30% MG+ 60% FG,
or
15% HG + 85% FG, where
HG = the average of the homework grades, except the two lowest ones
MG = the grade of the midterm
FG = the grade of the final exam
Date of the midterm: Wednesday, October 26, 2016 (for both groups), time and place: Lec 1 - 8-8h50AM (MS 6229); Lec 2 - 11-11h50 (in two rooms MS 5137 and MS 7608)
Date of the final exam: Lec 1: Friday, December 9, 2016, 3-6PM, place: TBA; Lec 2: Friday, December 9, 2016, 11h30AM-2h30PM, place: TBA.
Regrading for the homework papers, the midterm and the final should be requested within 2 weeks of their due date and exam date respectively. Any requests after this period will be not taken into consideration.
Homework sheets
Homework 1 - due to Friday, September 30, 2016