TEST_MIN
Test problems for minimization
TEST_MIN
is a Python library which
defines problems involving the minimization
of a scalar function of a scalar argument.
TEST_MIN can be useful for testing algorithms that
attempt to minimize a scalar function of a scalar argument.
Each problem has an index number, and there are a corresponding
set of routines, with names beginning with the index number, to:
-
evaluate f(x);
-
evaluate f'(x);
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evaluate f"(x);
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return the title of the problem;
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return a starting point;
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return a starting search interval;
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return the exact solution;
There is also a "generic" problem interface, whose routines all
begin with "P00". This allows the user to call all possible
problems in a single simple loop, by passing the desired index
number through the generic interface.
The functions can be invoked by an index number, and include:
-
f(x) = ( x - 2 )^2 + 1;
a PNG image;
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f(x) = x^2 + exp ( -x );
a PNG image;
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f(x) = x^4 + 2x^2 + x + 3;
a PNG image;
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f(x) = exp ( x ) + 0.01 / x;
a PNG image;
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f(x) = exp ( x ) - 2 * x + 0.01 / x - 0.000001 / x^2;
a PNG image;
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f(x) = 2 - x;
a PNG image;
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f(x) = ( x + sin ( x ) ) * exp ( -x^2 );
a PNG image;
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f(x) = 3 * x^2 + 1 + ( log ( ( x - pi )^2 ) ) / pi^4;
a PNG image;
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f(x) = x^2 - 10 sin ( x^2 - 3x + 2);
a PNG image;
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f(x) = cos(x)+5*cos(1.6*x)-2*cos(2*x)+5*cos(4.5*x)+7*cos(9*x);
a PNG image;
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f(x) = 1+|3x-1|;
a PNG image;
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
TEST_MIN is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
BRENT,
a Python library which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
LOCAL_MIN_RC,
a Python library which
finds a local minimum of a scalar function of a scalar variable,
without the use of derivative information,
using reverse communication (RC),
by Richard Brent.
Reference:
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Isabel Beichl, Dianne O'Leary, Francis Sullivan,
Monte Carlo Minimization and Counting: One, Two, Too Many,
Computing in Science and Engineering,
Volume 9, Number 1, January/February 2007.
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Richard Brent,
Algorithms for Minimization without Derivatives,
Dover, 2002,
ISBN: 0-486-41998-3,
LC: QA402.5.B74.
-
David Kahaner, Cleve Moler, Steven Nash,
Numerical Methods and Software,
Prentice Hall, 1989,
ISBN: 0-13-627258-4,
LC: TA345.K34.
-
Arnold Krommer, Christoph Ueberhuber,
Numerical Integration on Advanced Computer Systems,
Springer, 1994,
ISBN: 3540584102,
LC: QA299.3.K76.
-
Dianne O'Leary,
Scientific Computing with Case Studies,
SIAM, 2008,
ISBN13: 978-0-898716-66-5,
LC: QA401.O44.
-
LE Scales,
Introduction to Non-Linear Optimization,
Springer, 1985,
ISBN: 0-387-91252-5,
LC: QA402.5.S33.
Source Code:
You can go up one level to
the Python source codes.
Last revised on 07 December 2016.