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<html>
<head>
<title>
PRAXIS - Scalar Function Optimization
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PRAXIS <br> Scalar Function Optimization
</h1>
<hr>
<p>
<b>PRAXIS</b>
is a FORTRAN90 library which
minimizes a scalar function of a vector argument,
without needing derivative information,
by Richard Brent.
</p>
<p>
<b>PRAXIS</b> seeks an M-dimensional point X which minimizes a
given scalar function <b>F(X)</b>. The code is a refinement
of Powell's method of conjugate search directions. The user
does not need to supply the partial derivatives of the function
<b>F(X)</b>. In fact, the function <b>F(X)</b> need not be
smoothly differentiable.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>PRAXIS</b> is available in
<a href = "../../f77_src/praxis/praxis.html">a FORTRAN77 version</a> and
<a href = "../../f_src/praxis/praxis.html">a FORTRAN90 version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/brent/brent.html">
BRENT</a>,
a FORTRAN90 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.
</p>
<p>
<a href = "../../f_src/bvls/bvls.html">
BVLS</a>,
a FORTRAN90 library which
applies least squares methods to solve a linear system for which
lower and upper constraints may have been placed on every variable.
</p>
<p>
<a href = "../../f_src/compass_search/compass_search.html">
COMPASS_SEARCH</a>,
a FORTRAN90 library which
seeks the minimizer of a scalar function of several variables
using compass search, a direct search algorithm that does not use derivatives.
</p>
<p>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems.
</p>
<p>
<a href = "../../m_src/entrust/entrust.html">
ENTRUST</a>,
a MATLAB program which
solves problems in scalar optimization or nonlinear least squares.
</p>
<p>
<a href = "../../f_src/minpack/minpack.html">
MINPACK</a>,
a FORTRAN90 library which
solves systems of nonlinear equations, or the least squares minimization of the
residual of a set of linear or nonlinear equations.
</p>
<p>
<a href = "../../f_src/nl2sol/nl2sol.html">
NL2SOL</a>,
a FORTRAN90 library which
implements an adaptive nonlinear least-squares algorithm.
</p>
<p>
<a href = "../../f_src/test_opt/test_opt.html">
TEST_OPT</a>,
a FORTRAN90 library which
defines test problems
requiring the minimization of a scalar function of several variables.
</p>
<p>
<a href = "../../f_src/test_opt_con/test_opt_con.html">
TEST_OPT_CON</a>,
a FORTRAN90 library which
defines test problems for the minimization of a scalar function
of several variables, with the search constrained to lie within a specified hyper-rectangle.
</p>
<p>
<a href = "../../f_src/test_optimization/test_optimization.html">
TEST_OPTIMIZATION</a>,
a FORTRAN90 library which
defines test problems for the minimization of a scalar function
of several variables, as described by Molga and Smutnicki.
</p>
<p>
<a href = "../../f_src/toms611/toms611.html">
TOMS611</a>,
a FORTRAN90 library which
seeks the minimizer of a scalar functional
of multiple variables.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ul>
<li>
Richard Brent,<br>
Algorithms for Minimization without Derivatives,<br>
Dover, 2002,<br>
ISBN: 0-486-41998-3,<br>
LC: QA402.5.B74.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "praxis.f90">praxis.f90</a>, the source code.
</li>
<li>
<a href = "praxis.sh">praxis.sh</a>, commands to compile the
source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "praxis_prb.f90">praxis_prb.f90</a>, sample calling program.
</li>
<li>
<a href = "praxis_prb.sh">praxis_prb.sh</a>, commands to
compile, link, load and run the calling program.
</li>
<li>
<a href = "praxis_prb_output.txt">praxis_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>FLIN</b> is the function of one variable to be minimized by MINNY.
</li>
<li>
<b>MINFIT</b> computes the singular value decomposition of an N by N array.
</li>
<li>
<b>MINNY</b> minimizes a scalar function of N variables along a line.
</li>
<li>
<b>PRAXIS</b> seeks an N-dimensional minimizer X of a scalar function F(X).
</li>
<li>
<b>PRINT2</b> prints certain data about the progress of the iteration.
</li>
<li>
<b>QUAD</b> seeks to minimize the scalar function F along a particular curve.
</li>
<li>
<b>R8_HYPOT</b> returns the value of sqrt ( X^2 + Y^2).
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_SWAP</b> swaps the entries of two R8VECs.
</li>
<li>
<b>SORT</b> sorts a vector D and adjusts the corresponding columns of a matrix V.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 22 March 2012.
</i>
<!-- John Burkardt -->
</body>
</html>