Project of Optimization method for linear problem(Dual and Simplex method)

The written report consists of a PDF file of roughly 5 − 10 typed pages (excluding
figures, with reasonable spacing, font size, and font) that gives the background,
the main sources, an explanation of the method, any theoretical results about the
method that you choose to include, an overview of your implementation of the
method, and a description of the tests you performed and their results (including
an interpretation of those results). Typing the file in LaTeX is preferred (and
easier than using Word), but it is not required. A typical format might include the
following sections.
• Background: What is the mathematical problem that the numerical method
solves? What is an overview of how the method solves this problem? What
are the definitions and basic ideas required to understand this problem and
method?
• Description of the Method: How does the method work? What are the
assumptions on the input of the method (continuity, differentiability, etc.)?
Are there any error bounds for the method? If so, how accurate do you expect
the method to be (possibly depending on the input)? Are there different
versions of the method that improve it in some way?
• Code Implementation: How is the method implemented in software? Is it
any different than the mathematical description (say, due to avoiding roundoff error)? What functions did you write to support the main file, and why
did you choose to break it down in this manner?
• Testing and Results: What examples are you using to test your code?
Present at least one example in which your code works. Are there examples in
which your code fails to work? If so, why does that occur (think of Newton’s
method when f
0
(p) = 0, for example)? Include figures such as graphical depictions of the soluion or convergence plots, and always make sure to interpret
your results; a picture may be worth a thousand words, but you still need to
write a few of them! If your code does not work, then you should perform
extensive tests and make an informed guess at where the error likely occurs.
Think about the best way to display your data. A table is good for comparing
3data or if the data has high dimension; a colorful plot can show data more
clearly but is limited to three dimensions.
• Bibliography: A bibliography containing at least three references, at least
two of which must be from academic sources, must be included at the end
of the report. Each reference must contain the article name, author, year,
publication, and preferably a URL that can be used to access the source.
You are not required to use this exact layout for your written report, but it must
be an arrangement that makes sense to read and clearly conveys your ideas. If you
have any questions about the structure of your report, please ask!
3.2 The Code
The code portion of the project has requirements identical to those of the homework
assignments, and you should review the Code Guidelines thoroughly while writing
your code. The difference is that you are determining what examples are used to
demonstrate your code. To be specific, your code should consist of the following
parts.
• Main file: You should have one file whose name includes “main” that runs all
of your examples and produces the necessary output and figures. In particular,
every figure that is generated should be displayed (multiple figures can be
displayed by entering the command figure before a plot command).
• Function files: The rest of your files should be functions that implement the
method that you are studying and are used in the main file to generate the
results for the examples that you choose.
As usual, all code should have the informational header at the top and include
appropriate commenting. There is no restriction on the number of lines your code
should be, but you must have some code implementation of the method described
in your report. As a general rule, the amount of code required for a good project is
inversely proportional to the amount of theoretical description given in the written
report. If you state and prove several error estimates that clearly required time
and effort to write, then your code may be a short implementation with a couple
of meaningful examples (and their interpretation, most likely confirming the error
estimates). Conversely, if you have an extensive code implementation with many
good examples, some of which show the limits of the method’s usability, then your
written report may contain only a minimal description of the theory of the method.