test_opt_con/test_opt_con.html

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    <title>
      TEST_OPT_CON - Test Functions for Scalar Optimization, Constrained to a Hyper-Rectangle
    </title>
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    <h1 align = "center">
      TEST_OPT_CON <br> 
      Test Functions for Scalar Optimization <br>
      Constrained to a Hyper-Rectangle
    </h1>

    <hr>

    <p>
      <b>TEST_OPT_CON</b>
      is a FORTRAN90 library which
      defines a set of constrained global optimization problems.
    </p>

    <p>
      A typical constrained global optimization problem presents an M-dimensional
      hyper-rectangle bounded by A(1:M) <= X(1:M) <= B(1:M), and a scalar-valued
      function F(X).  The task is to find a point X within the hyper-rectangle
      at which the function takes its minimum value.
    </p>

    <p>
      This task is impossible, mathematically and in general.  However, the problems
      that can be solved mathematically are often not the ones encountered in
      real life.  Thus, it is useful to try to solve an impossible problem, since
      an approximate answer to such a problem can be all we can hope for or need.
    </p>

    <p>
      The functions defined include:
      <ol>
        <li>
          NM1: Niederreiter-McCurley function #1, M = 4;
        </li>
        <li>
          NM2: Niederreiter-McCurley function #2, M = 4;
        </li>
        <li>
          NM3: Niederreiter-McCurley function #3, M = 4;
        </li>
        <li>
          NM4: Niederreiter-McCurley function #4, M = 4;
        </li>
        <li>
          NM5: Niederreiter-McCurley function #5, M = 4;
        </li>
        <li>
          NM6: Niederreiter-McCurley function #6, M = 4;
        </li>
        <li>
          NM6: Niederreiter-McCurley function #6, M = 4;
        </li>
        <li>
          L02: Langerman function, M = 2;
        </li>
        <li>
          L10: Langerman function, M = 10;
        </li>
      </ol>
    </p>

    <p>
      For each function, the library includes a routine to evaluate the function,
      but also routines to return the limits of the hyper-rectangle, the
      spatial dimension, the solution, if known, and a title for the problem.
      These routines have a standard set of names based on the function index.
      For instance, for function #3, we have the routines:
      <ul>
        <li>
          <b>P03_AB</b> returns bounds for problem 3.
        </li>
        <li>
          <b>P03_F</b> returns the objective function value for problem 3.
        </li>
        <li>
          <b>P03_M</b> returns the spatial dimension for problem 3.
        </li>
        <li>
          <b>P03_SOL</b> returns known solutions for problem 3.
        </li>
        <li>
          <b>P03_TITLE</b> returns a title for problem 3.
        </li>
      </ul>
    </p>

    <p>
      Since the same interface is used for each function,
      if you wish to work with problem 6 instead, you simply change
      the "03" to "06" in your routine calls.
    </p>

    <p>
      If you wish to call <i>all</i> of the functions, you can write a concise
      program to do so by using the generic interface, in which the function
      names use the prefix <b>P00_</b>, and require the specific problem index
      to be supplied as an extra input argument:
      <ul>
        <li>
          <b>P00_AB</b> returns bounds for a problem specified by index.
        </li>
        <li>
          <b>P00_F</b> returns the objective function value for a problem specified by index.
        </li>
        <li>
          <b>P00_M</b> returns the spatial dimension for a problem specified by index.
        </li>
        <li>
          <b>P00_SOL</b> returns known solutions for a problem specified by index.
        </li>
        <li>
          <b>P00_TITLE</b> returns a title for a problem specified by index.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Licensing:
    </h3>

    <p>
      The computer code and data files described and made available on this
      web page are distributed under
      <a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
    </p>

    <h3 align = "center">
      Languages:
    </h3>

    <p>
      <b>TEST_OPT_CON</b> is available in
      <a href = "../../c_src/test_opt_con/test_opt_con.html">a C version</a> and
      <a href = "../../cpp_src/test_opt_con/test_opt_con.html">a C++ version</a> and
      <a href = "../../f77_src/test_opt_con/test_opt_con.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/test_opt_con/test_opt_con.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/test_opt_con/test_opt_con.html">a MATLAB version</a>.
    </p>

    <h3 align="center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f_src/asa047/asa047.html">
      ASA047</a>,
      a FORTRAN90 library which
      minimizes a scalar function of several variables using the Nelder-Mead algorithm.
    </p>

    <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/compass_search/compass_search.html">
      COMPASS_SEARCH</a>,
      a FORTRAN90 program which
      minimizes a scalar function of several variables using the compass search algorithm.
    </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
      minimizes a scalar function of several variables using trust-region methods.
    </p>

    <p>
      <a href = "../../m_src/fmincon/fmincon.html">
      FMINCON</a>,
      a MATLAB library which
      demonstrates the use of the <b>fmincon()</b> function to seek the minimizer
      of a function <b>f(x)</b> subject to a constraint.
    </p>

    <p>
      <a href = "../../m_src/nelder_mead/nelder_mead.html">
      NELDER_MEAD</a>,
      a MATLAB program which
      minimizes a scalar function of several variables using the Nelder-Mead algorithm,
      by Jeff Borggaard.
    </p>

    <p>
      <a href = "../../f_src/praxis/praxis.html">
      PRAXIS</a>,
      a FORTRAN90 library which
      implements the principal axis method of Richard Brent for minimization of
      a function without the use of derivatives.
    </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_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/toms178/toms178.html">
      TOMS178</a>,
      a FORTRAN90 library which
      optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.
    </p>

    <p>
      <a href = "../../f_src/toms611/toms611.html">
      TOMS611</a>,
      a FORTRAN90 library which
      can be used to seek the minimizer of a scalar functional
      of multiple variables.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Harald Niederreiter, Kevin McCurley,<br>
          Optimization of functions by quasi-random search methods,<br>
          Computing,<br>
          Volume 22, Number 2, 1979, pages 119-123.
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "test_opt_con.f90">test_opt_con.f90</a>, the source code.
        </li>
        <li>
          <a href = "test_opt_con.sh">test_opt_con.sh</a>,
          BASH commands to compile the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "test_opt_con_prb.f90">test_opt_con_prb.f90</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "test_opt_con_prb.sh">test_opt_con_prb.sh</a>,
          BASH commands to compile and run the sample program.
        </li>
        <li>
          <a href = "test_opt_con_prb_output.txt">test_opt_con_prb_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>P00_AB</b> returns bounds for a problem specified by index.
        </li>
        <li>
          <b>P00_F</b> returns the objective function value for a problem specified by index.
        </li>
        <li>
          <b>P00_M</b> returns the spatial dimension for a problem specified by index.
        </li>
        <li>
          <b>P00_PROBLEM_NUM</b> returns the number of problems.
        </li>
        <li>
          <b>P00_SOL</b> returns known solutions for a problem specified by index.
        </li>
        <li>
          <b>P00_TITLE</b> returns a title for a problem specified by index.
        </li>
        <li>
          <b>P01_AB</b> returns bounds for problem 1.
        </li>
        <li>
          <b>P01_F</b> returns the objective function value for problem 1.
        </li>
        <li>
          <b>P01_M</b> returns the spatial dimension for problem 1.
        </li>
        <li>
          <b>P01_SOL</b> returns known solutions for problem 1.
        </li>
        <li>
          <b>P01_TITLE</b> returns a title for problem 1.
        </li>
        <li>
          <b>P02_AB</b> returns bounds for problem 2.
        </li>
        <li>
          <b>P02_F</b> returns the objective function value for problem 2.
        </li>
        <li>
          <b>P02_M</b> returns the spatial dimension for problem 2.
        </li>
        <li>
          <b>P02_SOL</b> returns known solutions for problem 2.
        </li>
        <li>
          <b>P02_TITLE</b> returns a title for problem 2.
        </li>
        <li>
          <b>P03_AB</b> returns bounds for problem 3.
        </li>
        <li>
          <b>P03_F</b> returns the objective function value for problem 3.
        </li>
        <li>
          <b>P03_M</b> returns the spatial dimension for problem 3.
        </li>
        <li>
          <b>P03_SOL</b> returns known solutions for problem 3.
        </li>
        <li>
          <b>P03_TITLE</b> returns a title for problem 3.
        </li>
        <li>
          <b>P04_AB</b> returns bounds for problem 4.
        </li>
        <li>
          <b>P04_F</b> returns the objective function value for problem 4.
        </li>
        <li>
          <b>P04_M</b> returns the spatial dimension for problem 4.
        </li>
        <li>
          <b>P04_SOL</b> returns known solutions for problem 4.
        </li>
        <li>
          <b>P04_TITLE</b> returns a title for problem 4.
        </li>
        <li>
          <b>P05_AB</b> returns bounds for problem 5.
        </li>
        <li>
          <b>P05_F</b> returns the objective function value for problem 5.
        </li>
        <li>
          <b>P05_M</b> returns the spatial dimension for problem 5.
        </li>
        <li>
          <b>P05_SOL</b> returns known solutions for problem 5.
        </li>
        <li>
          <b>P05_TITLE</b> returns a title for problem 5.
        </li>
        <li>
          <b>P06_AB</b> returns bounds for problem 6.
        </li>
        <li>
          <b>P06_F</b> returns the objective function value for problem 6.
        </li>
        <li>
          <b>P06_M</b> returns the spatial dimension for problem 6.
        </li>
        <li>
          <b>P06_SOL</b> returns known solutions for problem 6.
        </li>
        <li>
          <b>P06_TITLE</b> returns a title for problem 6.
        </li>
        <li>
          <b>P07_AB</b> returns bounds for problem 7.
        </li>
        <li>
          <b>P07_F</b> returns the objective function value for problem 5.
        </li>
        <li>
          <b>P07_M</b> returns the spatial dimension for problem 7.
        </li>
        <li>
          <b>P07_SOL</b> returns known solutions for problem 7.
        </li>
        <li>
          <b>P07_TITLE</b> returns a title for problem 7.
        </li>
        <li>
          <b>P08_AB</b> returns bounds for problem 8.
        </li>
        <li>
          <b>P08_F</b> returns the objective function value for problem 8.
        </li>
        <li>
          <b>P08_M</b> returns the spatial dimension for problem 8.
        </li>
        <li>
          <b>P08_SOL</b> returns known solutions for problem 8.
        </li>
        <li>
          <b>P08_TITLE</b> returns a title for problem 8.
        </li>
        <li>
          <b>R8COL_UNIFORM</b> fills an R8COL with scaled pseudorandom numbers.
        </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 17 February 2012.
    </i>

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