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1 <html>
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2 <head>
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3 <title>
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4 Netlab Reference Manual linemin
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5 </title>
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6 </head>
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7 <body>
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8 <H1> linemin
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9 </H1>
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10 <h2>
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11 Purpose
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12 </h2>
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13 One dimensional minimization.
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14
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15 <p><h2>
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16 Description
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17 </h2>
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18 <CODE>[x, options] = linemin(f, pt, dir, fpt, options)</CODE> uses Brent's
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19 algorithm to find the minimum of the function <CODE>f(x)</CODE> along the
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20 line <CODE>dir</CODE> through the point <CODE>pt</CODE>. The function value at the
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21 starting point is <CODE>fpt</CODE>. The point at which <CODE>f</CODE> has a local minimum
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22 is returned as <CODE>x</CODE>. The function value at that point is returned
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23 in <CODE>options(8)</CODE>.
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24
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25 <p><CODE>linemin(f, pt, dir, fpt, options, p1, p2, ...)</CODE> allows
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26 additional arguments to be passed to <CODE>f()</CODE>.
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27
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28 <p>The optional parameters have the following interpretations.
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29
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30 <p><CODE>options(1)</CODE> is set to 1 to display error values.
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31
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32 <p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
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33 of <CODE>x</CODE> at the solution.
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34
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35 <p><CODE>options(3)</CODE> is a measure of the precision required of the objective
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36 function at the solution. Both this and the previous condition must be
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37 satisfied for termination.
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38
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39 <p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.
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40
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41 <p><h2>
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42 Examples
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43 </h2>
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44 An example of the use of this function to find the minimum of a function
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45 <CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>conjgrad</CODE>
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46 <PRE>
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47
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48 x = linemin(f, xold, sd, fold, lineoptions);
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49 </PRE>
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50
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51
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52 <p><h2>
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53 Algorithm
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54 </h2>
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55
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56 Brent's algorithm uses a mixture of quadratic interpolation and golden
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57 section search to find the minimum of a function of a single variable once
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58 it has been bracketed (which is done with <CODE>minbrack</CODE>). This is adapted
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59 to minimize a function along a line.
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60 This implementation
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61 is based on that in Numerical Recipes.
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62
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63 <p><h2>
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64 See Also
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65 </h2>
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66 <CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE><hr>
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67 <b>Pages:</b>
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68 <a href="index.htm">Index</a>
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69 <hr>
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70 <p>Copyright (c) Ian T Nabney (1996-9)
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71
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72
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73 </body>
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74 </html> |
