Math 164: Optimization

Spring 2016

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). We will perform proofs as well, hence the course is not only computation oriented. For instance, we will prove the convergence of the algorithms that we consider.

Instructor: Alpár R. Mészáros, MS 5230 (check the e-mail address on my webpage or on CCLE)

Schedule of classes: MWF - 8-8h50AM

Office hours: M-W, 9h00-10h30AM

Location: MS building, 5117

TA: Zhimin Peng, MS 7630 (check e-mail address on CCLE)

Discussion: Tuesday, 8-8h50AM, same room as for the lecture

TA's office hour: 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.

Homeworks will be assigned weekly 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. Please note that late- or no homeworks 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 homeworks. In this case, everybody from the group has to submit his 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 two midterms(see the precise dates 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. You can chose the scheme which gives you higher final score:
10% HG + 40% ((MG1+MG2)/2) + 50% FG,
or
10% HG + 25% max(MG1;MG2) + 65% FG, where

HG = the average of the homework grades, except the two lowest ones

MG1, MG2 = the two midterm grades

FG = the grade of the final exam

Date of the first midterm: Wednesday, April 20, 2016, place: FRANZ 2258A

Date of the second midterm: Wenesday, May 18, 2016, place: FRANZ 2258A

Date of the final exam: Thursday, June 9, 2016, 3-6PM, place: BOELTER 5440

Regrading for the homeworks, midterms 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