AMSC 607 / CMSC 764 Homework 2, Fall 2008
Due 2pm Tuesday October 7
Assignment: Write a Matlab function that minimizes a function using New-
tonās method with trust region.
Follow the directions in parts (ii), (iii), (iv), and (v) of Nash and Soferās
Problem 10.17, p.340 (the 106th page of the pdf file). (In my hard-copy of
the book, it is Problem 16, p.327.) It begins, āWrite a computer program for
minimizing a multivariate function....ā
Notes:
ā¢Compute an eigendecomposition of each Hessian matrix and then use the
method of Homework 1 to find the correct value of Ī³.
ā¢Your implementation of Newtonās method should be in a function newtonmin
which can be easily applied to other functions f(x) with xā Rnand n
arbitrary.
ā¢The function newtonmin should be well-documented, as if it were a library
code. In particular, documentation at the top of the function should
include:
ā purpose of co de, since this is certainly the first thing a user wants
to know!
ā name of author, since it provides someone to whom bugs can be
reported and questions asked.
ā date of the original code and a list of later modifications,
since it gives information such as whether the code is likely to run
under the current computer environment and whether it might in-
clude the latest advances.
ā description of each input parameter, so that a user knows what
information needs to be provided and in what format.
ā description of each output parameter, so that a user knows
what information will be yielded.
ā brief description of the method and references, to help a user
decide whether the method fits his/her needs.
In-line documentation should identify the major sections of the code
and provide some detail on the method used. It is important in specifying
the algorithm, identifying bugs, and providing information to someone
who might need to modify the software in order to solve a slightly different
problem.
Note that the documentation should be an integral part of the code; in
other words, it is not enough to include it in a separate document, because
a potential user might not have access to that document.
1
