Instructor: Katy Craig, MS 7354, katy•craig•math at gmail • com

Teaching Assistant: Tyler Arant, MS 2361, tylerarant at math • ucla • edu

Lecture/Section/Office Hours: Times and Locations

Textbook: I. Griva, S. Nash, and A. Sofer, Linear and Nonlinear Optimization, second edition.

Other Recommended References:

D. Luenberger and Y. Ye, Linear and Nonlinear Programming. (Free, if you download from the campus network)

S. Boyd and L. Vandenberghe, Convex Optimization. (Free)

Exams: There will be two midterms and one final exam. The examinations will be closed book and closed note. There will be no retaking or rescheduling of exams under any circumstances, as the grading scheme allows you to drop your lowest midterm score.

First Midterm: Wednesday, April 29th, 8:00-8:50AM

Second Midterm: Wednesday, May 27th, 8:00-8:50AM

Final Exam: Friday, June 12th, 11:30AM-2:30PM

Grading Scheme: homework: 10%, highest midterm score: 40%, final: 50%

If you have questions about the grading of any assignment or exam, you have one week after it is handed back to request a regrade.

Prerequisites: Math 115A

Outline of Course:

Part 1: linear optimization                    Part 2: nonlinear optimization

• fundamentals of optimization            • unconstrained optimization

• geometry of linear programming       • linear (in)equality constraints

• the simplex method                          • Lagrange multipliers

• duality                                               • nonlinear (in)equality constraints

Syllabus:

                             read by today         topic

1    Mar 30 (M):     1.1-1.5                     Optimization: applications and the need for theory

2    Apr 1 (W):        2.2                           Feasibility and optimality

3    Apr 3 (F):         2.3 (without 2.3.1)    Convexity, part 1

4    Apr 6 (M):        -                               Convexity, part 2

5    Apr 8 W):        3.1                            Linear constraints and the geometry of the feasible region

6    Apr 10 (F):      4.1                            Geometry of linear programming

7    Apr 13 (M):     4.2                            Standard form

8    Apr 15 (W):     4.3                            Basic solutions and extreme points, part 1

9    Apr 17 (F):      -                                Basic solutions and extreme points, part 2

10  Apr 20 (M):     4.4                            Representation of solutions, part 1

11  Apr 22 (W):     -                                Representation of solutions, part 2

12  Apr 24 (F):      5.2                            The simplex method, part 1

13  Apr 27 (M):      -                               The simplex method, part 2

14  Apr 29 (W):     -                                First midterm, covering lectures 1-12

15  May 1 (F):       -                                The simplex method, part 3

16  May 4 (M):      6.1, 6.2                     The dual linear program, interpretation of the dual

17  May 6 (W):     -                                Duality theory

18  May 8 (F):       6.2.1, 6.2.2              Complementary slackness, part 1

19  May 11 (M):    -                               Complementary slackness, part 2

20  May 13 (W):    B.4, 2.3.1, 2.6          Derivatives and convexity

21  May 15 (F):     B.7                           More derivatives and convexity

22  May 18 (M):     3.2                          Null and range spaces

23  May 20 (W):    11.2                        Optimality conditions: unconstrained optimization

24  May 22 (F):     14.2                         Optimality conditions: linear equality constraints, part 1

25  May 25 (M):    -                               Happy Memorial Day!

26  May 27 (W):    -                               Second midterm, covering lectures 13-24

27  May 29 (F):     -                               Optimality conditions: linear equality constraints, part 2

28  June 1 (M):     14.3                          Lagrange multipliers and the Lagrangian, part 1   

29  June 3 (W):     -                               Lagrange multipliers and the Lagrangian, part 2

30  June 5 (F):      14.4                          Optimality conditions: linear inequality constraints

-  June 12 (F):                                       Final exam, covering lectures 1-30, 11:30AM-2:30PM