Math 5750 - Math 6880: Optimization

Instructor: Yekaterina Epshteyn

Lectures: MWF 11:50 - 12:40 pm, WEB 1450

Office Hours (tentative, it may be some changes)

M 12:50-1:50, F 1:00-1:30 pm, or by appointment
Office: LCB 337
E-mail: epshteyn@math.utah.edu

Textbook and References

Main Textbooks: J.Nocedal and S.Wright, Numerical Optimization, Springer, second edition

References:

P. Ciarlet, Introduction to numerical linear algebra and optimization, Cambridge University Press

C.T. Kelley, Iterative Methods for Optimization, SIAM

Prerequisites for Math 5750 - Math 6880

Linear algebra (Math 2270 or similar), vector calculus (Math 2210 or similar) and basic Matlab knowledge

Homework

Homework will be assigned (probably once in two weeks) and collected, and will include theoretical analysis and computational assignments. The computational part should be done using MATLAB, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows. The full set of manuals is on the web in html format. The "Getting Started" manual is a good place to begin and is available in Adobe PDF format.

5750 - 6880 Tentative Topics:

Unconstrained optimization: Necessary and sufficient optimality conditions; Newton's method; Line search; Quasi-Newton methods, non-linear least squares; Adjoint state method (for computing derivatives)

Constrained optimization: Constraints qualifications; Optimality conditions; Trust region methods; Linear programming (simplex and interior point methods); Quadratic programming

Other optimization methods

ADA Statement

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.

Grading: Homework 65% and one Final Written Exam (TBA) 35%


 

Tentative (it may be some changes) weekly\biweekly plan:

  • August 20 - August 31:
    • Introduction: 1D; R^n; unconstrained optimization; necessary and sufficient conditions for local/global minimum; Newton's method in R^1 and R^n; convergence of Newton's method
    Textbook (to read): Chapter 1, Chapter 2: Section 2.1, Chapter 3: pages 44-46 (Newton's method)

  • September 5 - September 30:
    • Line search methods, convergence results for line search methods; Quasi-Newton methods, BFGS; Linear Conjugate Gradient Method; (practical considerations and convergence theory)
    Textbook (to read): Chapter 3, Chapter 6, Chapter 5

  • October 1 - October 17 (October 7 - October 14 is the Fall Break):
    • Linear and Nonlinear Least-Squares Problems and Algorithms
    Textbook (to read): Chapter 10

  • October 22 - October 29:
    • Approximations of the Derivatives; Nonlinear Equations
    Textbook (to read): Chapter 8; Chapter 11

  • October 29 - November 9:
    • Constrained Optimization Problems: Linear Programming: The Simplex Method
    Textbook (to read): Chapter 13

  • November 9 - December 7:
    • Constrained Optimization Problems: Nonlinear Programming; Quadratic Programming
    Textbook (to read): Chapter 16

    Homework due dates will be announced and posted


     

  • Homework 1 
  • Homework 2 
  • Homework 3 
  • Homework 4