[CMSC 455] | [Syllabus] | [Lecture Notes] | [Homework] | [Projects] | [Files] | [Notes, all]

CMSC 455 Project, 100 points, find minimum

Do not talk to other students about the project.
You may use gmp, BigDecimal, MatLab, Maple, Mathematica or other
existing software, and any software from the course WEB site.
(Slightly different from previous semesters.)

Given the equation:

z = exp(sin(60.0*x)) + sin(50.0*exp(y)) +
    sin(80.0*sin(x)) + sin(sin(70.0*y)) -
    sin(10.0*(x+y)) + (x*x+y*y)/4.0

Find the global minimum -1 < x < 1 , -1 < y < 1

There are many local minima, do not get stuck in one of them.
A global search with dx and dy <= 0.001 should be in the
global minimum.
From inspection, the minimum z is roughly between -3 and -4

From the global search starting point, use optimization.
Do not allow dx, dy to get too small, roundoff error if less than
1.0E-16  in 64 bit floating point
1.0E-100 in multiple precision


Print your x and y and z.
I would expect, all to the same number of digits accuracy.

Your points are based on the accuracy of your computed
"x", "y", "z".
Your largest error in x, y, or z rounded to significant digits:
  2 digits  50 points
  3 digits  70 points
  4 digits  75 points
  5 digits  80 points
  6 digits  85 points
  7 digits  86 points
  8 digits  87 points
  9 digits  88 points
 10 digits  89 points
 11 digits  90 points
 12 digits  91 points
 13 digits  92 points
 14 digits  93 points
 15 digits  94 points
 16 digits  95 points
100 digits 100 points

Submitting your Project

 The project source and output is to be submitted on GL as 
   submit cs455 proj list-of-files
   etc.

 The list-of-files should include source code and output
 and other files that were used.
 Do not submit executable file(s).

 Use a language of your choice on an operating system
 of your choice, unless otherwise stated. Talk to the
 instructor if your language choice is not one of:
 Ada 95, C, C++, Fortran 95, Java, Python, Scala, SML, MATLAB,
 Maple, Mathematica, or similar available language or product.

 The goal of the project is to give you a useful
 numeric code that you can apply as needed to future
 tasks. This includes converting a working numeric code
 to your language of choice or being able to interface
 some working numeric code with your language of choice.

 Copying of a project results in zero points for everyone
 involved in copying. Be sure to check your own answers
 by using several languages or several implementations.
 You may want to do the global search in a language
 that is fast, submit that code, and then start the
 multiple precision at the x,y found in the global search
 with a small dx,dy.

A crude plot of z vs x,y is

A smaller dx,dy plot

Other links

• CMSC 455 home page
• Syllabus - class dates and subjects, homework dates, reading assignments
• Homework assignments - the details
• Projects -
• Partial Lecture Notes, one per WEB page
• Partial Lecture Notes, one big page for printing
• Downloadable samples, source and executables
• Some brief notes on Matlab
• Some brief notes on Fortran 95
• Some brief notes on Python
• Some brief notes on Ada 95
• An Ada math library (gnatmath95)
• Finite difference approximations for derivatives
• Reference pages on Taylor series, identities,
  coordinate systems, differential operators

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Last updated 6/21/2016