Newton's Method with Trust Region Homework Assignment for AMSC 607 and CMSC 764, Fall 2008, Assignments of Mathematics

Download Newton's Method with Trust Region Homework Assignment for AMSC 607 and CMSC 764, Fall 2008 and more Assignments Mathematics in PDF only on Docsity! AMSC 607 / CMSC 764 Homework 2, Fall 2008 Due 2pm Tuesday October 7 Assignment: Write a Matlab function that minimizes a function using New- ton’s method with trust region. Follow the directions in parts (ii), (iii), (iv), and (v) of Nash and Sofer’s 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, “Write a computer program for minimizing a multivariate function....” Notes: • Compute an eigendecomposition of each Hessian matrix and then use the method of Homework 1 to find the correct value of γ. • Your implementation of Newton’s method should be in a function newtonmin which can be easily applied to other functions f(x) with x ∈ Rn and n arbitrary. • 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: – purpose of code, since this is certainly the first thing a user wants to know! – name of author, since it provides someone to whom bugs can be reported and questions asked. – 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. – description of each input parameter, so that a user knows what information needs to be provided and in what format. – description of each output parameter, so that a user knows what information will be yielded. – 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