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1 <html>
2 <head>
3 <title>
4 Netlab Reference Manual quasinew
5 </title>
6 </head>
7 <body>
8 <H1> quasinew
9 </H1>
10 <h2>
11 Purpose
12 </h2>
13 Quasi-Newton optimization.
14
15 <p><h2>
16 Description
17 </h2>
18 <CODE>[x, options, flog, pointlog] = quasinew(f, x, options, gradf)</CODE>
19 uses a quasi-Newton
20 algorithm to find a local minimum of the function <CODE>f(x)</CODE> whose
21 gradient is given by <CODE>gradf(x)</CODE>. Here <CODE>x</CODE> is a row vector
22 and <CODE>f</CODE> returns a scalar value.
23 The point at which <CODE>f</CODE> has a local minimum
24 is returned as <CODE>x</CODE>. The function value at that point is returned
25 in <CODE>options(8)</CODE>. A log of the function values
26 after each cycle is (optionally) returned in <CODE>flog</CODE>, and a log
27 of the points visited is (optionally) returned in <CODE>pointlog</CODE>.
28
29 <p><CODE>quasinew(f, x, options, gradf, p1, p2, ...)</CODE> allows
30 additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>.
31
32 <p>The optional parameters have the following interpretations.
33
34 <p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error
35 values in the return argument <CODE>errlog</CODE>, and the points visited
36 in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0,
37 then only warning messages are displayed. If <CODE>options(1)</CODE> is -1,
38 then nothing is displayed.
39
40 <p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
41 of <CODE>x</CODE> at the solution. If the absolute difference between
42 the values of <CODE>x</CODE> between two successive steps is less than
43 <CODE>options(2)</CODE>, then this condition is satisfied.
44
45 <p><CODE>options(3)</CODE> is a measure of the precision required of the objective
46 function at the solution. If the absolute difference between the
47 objective function values between two successive steps is less than
48 <CODE>options(3)</CODE>, then this condition is satisfied.
49 Both this and the previous condition must be
50 satisfied for termination.
51
52 <p><CODE>options(9)</CODE> should be set to 1 to check the user defined gradient
53 function.
54
55 <p><CODE>options(10)</CODE> returns the total number of function evaluations (including
56 those in any line searches).
57
58 <p><CODE>options(11)</CODE> returns the total number of gradient evaluations.
59
60 <p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.
61
62 <p><CODE>options(15)</CODE> is the precision in parameter space of the line search;
63 default <CODE>1e-2</CODE>.
64
65 <p><h2>
66 Examples
67 </h2>
68 An example of
69 the use of the additional arguments is the minimization of an error
70 function for a neural network:
71 <PRE>
72
73 w = quasinew('neterr', w, options, 'netgrad', net, x, t);
74 </PRE>
75
76
77 <p><h2>
78 Algorithm
79 </h2>
80
81 The quasi-Newton algorithm builds up an
82 approximation to the inverse Hessian over a number of steps. The
83 method requires order W squared storage, where W is the number of function
84 parameters. The Broyden-Fletcher-Goldfarb-Shanno formula for the
85 inverse Hessian updates is used. The line searches are carried out to
86 a relatively low precision (1.0e-2).
87
88 <p><h2>
89 See Also
90 </h2>
91 <CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr>
92 <b>Pages:</b>
93 <a href="index.htm">Index</a>
94 <hr>
95 <p>Copyright (c) Ian T Nabney (1996-9)
96
97
98 </body>
99 </html>