CAAM 454 / 554
Iterative Methods for Systems of Equations and Unconstrained Optimization

Spring 2020 · Rice University


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ABOUT THIS COURSE:

 Iterative methods for linear systems of equations including Krylov subspace methods; Newton and Newton-like methods for nonlinear systems of equations; Gradient and Newton-like methods for unconstrained optimization and nonlinear least squares problems; techniques for improving the global convergence of these algorithms; linear programming duality and primal-dual interior-point methods.

The course title for CAAM454 / 554 used to be Numerical Analysis II, but was renamed Iterative Methods for Systems of Equations and Unconstrained Optimization in Spring 2020 to better reflect the course content. The overall content and structure of CAAM454 / 554 remained unchanged.

LECTURES:

 Tues/Thurs 2:30pm-3:45pm, SEW 307

INSTRUCTOR:

 Matthias Heinkenschloss (heinken_AT_rice.edu), Duncan Hall 3088, (713) 348-5176
Office hours: M 1:00-2:00pm, DH 3088, or by appointment.

454 or 554?

 Students may take this course as either CAAM 454 or 554: both meet for the same T/Th lectures, but CAAM 554 will include more theoretical homework and exam problems, and potentially some supplemental lectures with additional theoretical material. CAAM graduate students must enroll in CAAM 554; others comfortable writing rigorous mathematical proofs may also consider this option. Students cannot take both CAAM 454 and 554 for credit.

PROBLEM SETS:

 Problem sets will be assigned roughly once a week. There will be two pledged problem sets/ exams.
On unpledged assignments you may collaborate, but your write-up must be your own independent work. Exams/pledged homework assignments may be timed and `closed book', and you are not allowed to discuss exams/ pledged assignments with anyone but your instructor. Transcribed solutions are unacceptable; you may not consult solutions from previous sections of this class.

GRADING:

 60% unpledged problem sets, 40% pledged (Class participation, improving performance on the pledged homeworks, and feedback on the handouts will be considered when assigning borderline grades.)

LATE POLICY:

 You may turn in two unpledged problem sets one class period late without penalty. Subsequent late assignments will be penalized 20% each. Homework will not be accepted more than one class period late without a written excuse. This implies that you may not use two `lates' on one assignment. Pledged assignments/exams must be turned in on time.

COURSE NOTES:

 Course notes will be posted on CANVAS. The lectures page contains required and additional reading for the lectures.

SYLLABUS:

 pdf

RECOMMENDED
READING

 J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, 1996.
P. E. Gill, W. Murray and M. H. Wright, Practical optimization, SIAM, 2019.
C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995.
C. T. Kelley, Iterative Methods for Optimization, SIAM, 1999.
J. Nocedal and S. J. Wright, Numerical Optimization(second edition), Springer Verlag, 2006.
Y. Saad, Iterative methods for sparse linear systems(2nd edition)}, SIAM, 2003.
L. N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997.


Any student with a disability requiring accommodation in this course is encouraged
to contact the instructor during the first week of class, and also to contact
Disability Support Services in the Ley Student Center.


http://www.caam.rice.edu/~caam454    http://www.caam.rice.edu/~caam554