Math 164 Lecture 1

Winter 2010

Optimization

Lecture Meeting Time: MWF 10:00am-10:50am
Lecture Location: MS 5138

Instructor: Luminita Vese
Office: MS 7620 D
Office hours before the final: Tuesday, 11.30-2.30pm.
E-mail: lvese@math.ucla.edu

Virtual Office Hours
Class Web Page: http://www.math.ucla.edu/~lvese/164.1.10w/

Discussion Section Information
Section IDSectionClassroomTimeTA Name
2626292112aMS 5138 Tuesday 10:00am-10:50am Melissa TONG

T.A. E-mail: meltong@math.ucla.edu
T.A. Office: MS 6146.
T.A. office hours: Tuesday 11-12 and 2:30-3:30.

Textbook: S. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw-Hill, available at the student bookstore. Please check the Errata here:.

Other recommended references:

  • S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press 2004 online version.
  • P.E. Gill, W. Murray and M.H. Wright, Practical Optimization, Academic Press Limited 1981.
  • J. Nocedal, S.J. Wright, Numerical Optimization, Springer Verlag.

    Requisite: course Math 115A.

    Course Description: Fundamentals of optimization. Linear programming: basic solutions, simplex method, duality theory. Unconstrained optimization, Newton's method for minimization. Nonlinear programming, optimality conditions for constrained problems. Additional topics from linear and nonlinear programming.

    General Course Information
    General Course Outline

    Homework Policy: Homework will be assigned every week and will be collected the following week on WEDNESDAY. No late homework will be accepted.
    The lowest homework grade will be dropped and will not count for the final grade.
    You are encouraged to solve as many problems as you can from the textbook, and not only those from the homework assignments.
    There will be theoretical and some computational assignments. For the computational assignments, you can open a computer account and work at the PIC Lab. Include with your homework the code of the computational assignment used to produce the results and explanations.

    Examinations: One midterm exam and one final exam. The examinations are closed-book and closed-note. No exams at a time other than the designated ones will be allowed (exceptions for illness with document proof, or emergency).
    Midterm: Wednesday, February 17, time 10-11am, MS 5138.
    - Sample midterm questions [1] [2] (solutions posted below in Handouts:)
    - Sections covered for the midterm:

    Final Exam: Thursday, March 18, 2010, 8:00am-11:00am
  • Office hours before the final: Tuesday, March 16, 2010, at MS 7620-D, time: TBA
  • ALL sections are covered for the final. However, more questions will be given from topics covered after the midterm.
    Sections covered before the midterm: 1, 2.2-2.4, 3.1, 4.1-4.4, 5.2, 6.1-6.2
    Sections covered after the midterm: 6.2.1, 2.3.1, 2.6, 2.7 (except the convergence analysis), 2.7.1, 10.2, 10.3 (except the convergence analysis), 3.2, 14.1, 14.2, 14.3, 14.4, 14.5. (Lemma 14.5 and Thm. 14.4 are not included in the final).

    - Sample problems for the final exam (thanks to Prof. Robert Brown): page [1] page [2] page [3]
    - Solutions to the sample final problems: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

    Grading Policy: Hw 25%, Midterm 25%, Final 50%

    Useful Links:
  • PIC Lab: Boelter Hall 2817 http://www.pic.ucla.edu/piclab/
  • MATLAB Documentation (thanks to Prof. C. Anderson, UCLA)
  • Numerical Recipes (see in particular Chapters 10 and 15 from the Numerical Recipes).
  • Getting started with MATLAB
  • UCLA problem of the week

    Handouts:
  • Example from the lecture on the simplex method
  • General form of the simplex method (thanks to Prof. Andrea Brose).
  • Sample midterm questions [1] [2] (thanks to Prof. Robert Brown)
    Sample midterm solutions [1] [1] [2] [3](a,b) [3](c) [4](a,b) [5](a) [5](b) [5](c)
  • Midterm solutions: Midterm solutions

  • Sample problems for the final exam (thanks to Prof. Robert Brown): page [1] page [2] page [3]
    - Solutions to the sample final problems: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
  • Solution to problem #6, page 446: #6, page 446
  • Summary of sufficient conditions for local minimizers for non-linear optimization Summary

    Weekly Homework Assignments:

    HW #1: due on Wednesday, January 13
    HW1.pdf

    HW #2: due on Wednesday, January 20
    HW2.pdf

    HW #3: due on Wednesday, January 27
    HW3.pdf

    HW #4: due on Wednesday, February 3
    HW4.pdf

    HW #5: due on Wednesday, February 10
    HW5.pdf

    HW #6: due on Wednesday, February 17
    HW6.pdf

    HW #7: due on Friday, February 26
    HW7.pdf

    HW #8: due on Friday, March 5
    HW8.pdf

    HW #9: due on Friday, March 12
    HW9.pdf