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