Math 164 Lecture 2

Fall 2005

Optimization

Lecture Meeting Time: MWF 1:00P-1:50P
Lecture Location: MS 6229

Instructor: Luminita Vese
Office: MS 7620 D

OFFICE HOURS BEFORE THE FINAL EXAM:

  • Wednesday 2-4pm in MS 7620-D
  • Thursday 2-4pm in MS 6201 (start with a review session) and continue in MS 7620-D.
  • See sample final questions below (NOTE: there may be a typo in the solution for problem #9).
  • REMINDER: Final exam on Friday, Dec. 16, time 8-11am, in MS 6229.

    E-mail: lvese@math.ucla.edu

    Virtual Office Hours
    Class Web Page: http://www.math.ucla.edu/~lvese/164.2.05f/

    Discussion Section Information
    Section IDSectionClassroomTimeTA Name
    2626292112aMS 6229 Tuesday 1:00P-1:50P ROY, Tristan

    T.A. E-mail: triroy@math.ucla.edu
    T.A. Office: MS 3975.
    T.A. office hours: Tuesday 2-3pm, or by appointment.

    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: The 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 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. You may also send by e-mail your code to the T.A.

    Examinations: One midterm exam and one final exam.
    Midterm: Wednesday November 9, 2005, 1.00pm-2.00pm (lecture).
    - Sample midterm questions [1] [2] (solutions posted below in Handouts:)

    Final: REMINDER: Friday, December 16, 2005, 8:00am-11:00am, room MS 6229.
    - The final is a closed-book and closed-note exam. No exam at a time other than the designated ones will be allowed (exceptions for illness with document proof, or emergency).
    - Additional office hours and review session will be scheduled during the week of finals (we discuss this on Friday, last day of lectures).
    - 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]
    - All sections and topics are covered for the final. However, more questions will be given from the second part (topics covered after the midterm).
    Sections covered for the final exam:
    - 1.2-1.5, 2.2-2.3, 3.1, 4.1-4.4, 5.2 (already covered for the midterm)
    - 6.1, 6.2, 6.2.1 (section 6.2.2. is not included)
    - Appendices A6, B4, B5, B6, B7.
    - 2.3.1, 2.6,
    - 2.7 (except the convergence thm.), 2.7.1,
    - 3.2
    - 10.2, 10.3 (except Thm. 10.1)
    - 14.2, 14.3 (only what is presented on page 437, not the discussion on the perturbed problem)
    - 14.4 (read also lemma 14.5, but this Lemma is not included for the final)
    - 14.5 (just to know the stated results, and apply them to a specific example)

    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).

    Grading Policy: Hw 20%, Midterm 30%, 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
  • 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) [3](d) [4](a,b) [5](a) [5](b) [5](c)
  • 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, October 5, 2005.
    HW1.pdf

    HW #2: due on Wednesday, October 12, 2005.
    HW2.pdf

    HW #3: due on Wednesday, October 19, 2005.
    HW3.pdf

    HW #4: due on Wednesday, October 26, 2005.
    HW4.pdf

    HW #5: due on Wednesday, November 2, 2005.
    HW5.pdf

    HW #6: due on Wednesday, November 9, 2005.
    HW6.pdf

    HW #7: due on Wednesday, November 16, 2005. DEADLINE EXTENSION UNTIL FRIDAY
    HW7.pdf

    HW #8: due on Wednesday, November 23, 2005.
    HW8.pdf

    HW #9: due on Friday, Dec. 2nd, 2005. (note different day)
    HW9.pdf

    HW #10: due on Friday, December 9 (no late homework accepted)
    Problems: Page 434, # 1, #2, #9, and page 307, #6.
    HW10.pdf