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<title>fminsearchbnd_demo</title>
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<h2>Contents</h2>
<div>
<ul>
<li><a href="#1">Optimization of a simple (Rosenbrock) function, with no constraints</a></li>
<li><a href="#2">Only lower bound constraints</a></li>
<li><a href="#3">Only upper bound constraints</a></li>
<li><a href="#4">Dual constraints</a></li>
<li><a href="#5">Mixed constraints</a></li>
<li><a href="#6">Provide your own fminsearch options</a></li>
<li><a href="#7">Exactly fix one variable, constrain some others, and set a tolerance</a></li>
<li><a href="#8">All the standard outputs from fminsearch are still returned</a></li>
</ul>
</div>
<h2>Optimization of a simple (Rosenbrock) function, with no constraints<a name="1"></a></h2><pre class="codeinput">rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;
<span class="comment">% With no constraints, operation simply passes through</span>
<span class="comment">% directly to fminsearch. The solution should be [1 1]</span>
xsol = fminsearchbnd(rosen,[3 3])
</pre><pre class="codeoutput">
xsol =
0.99998 0.99995
</pre><h2>Only lower bound constraints<a name="2"></a></h2><pre class="codeinput">xsol = fminsearchbnd(rosen,[3 3],[2 2])
</pre><pre class="codeoutput">
xsol =
2 4
</pre><h2>Only upper bound constraints<a name="3"></a></h2><pre class="codeinput">xsol = fminsearchbnd(rosen,[-5 -5],[],[0 0])
</pre><pre class="codeoutput">
xsol =
-1.0447e-13 -1.4451e-08
</pre><h2>Dual constraints<a name="4"></a></h2><pre class="codeinput">xsol = fminsearchbnd(rosen,[2.5 2.5],[2 2],[3 3])
</pre><pre class="codeoutput">
xsol =
2 3
</pre><h2>Mixed constraints<a name="5"></a></h2><pre class="codeinput">xsol = fminsearchbnd(rosen,[0 0],[2 -inf],[inf 3])
</pre><pre class="codeoutput">
xsol =
2 3
</pre><h2>Provide your own fminsearch options<a name="6"></a></h2><pre class="codeinput">opts = optimset(<span class="string">'fminsearch'</span>);
opts.Display = <span class="string">'iter'</span>;
opts.TolX = 1.e-12;
opts.MaxFunEvals = 100;
n = [10,5];
H = randn(n);
H=H'*H;
Quadraticfun = @(x) x*H*x';
<span class="comment">% Global minimizer is at [0 0 0 0 0].</span>
<span class="comment">% Set all lower bound constraints, all of which will</span>
<span class="comment">% be active in this test.</span>
LB = [.5 .5 .5 .5 .5];
xsol = fminsearchbnd(Quadraticfun,[1 2 3 4 5],LB,[],opts)
</pre><pre class="codeoutput">
Iteration Func-count min f(x) Procedure
0 1 173.731
1 6 172.028 initial simplex
2 8 162.698 expand
3 9 162.698 reflect
4 11 151.902 expand
5 13 138.235 expand
6 14 138.235 reflect
7 16 126.604 expand
8 17 126.604 reflect
9 19 97.3266 expand
10 20 97.3266 reflect
11 21 97.3266 reflect
12 22 97.3266 reflect
13 24 73.7178 expand
14 25 73.7178 reflect
15 26 73.7178 reflect
16 28 50.8236 expand
17 29 50.8236 reflect
18 31 41.6294 expand
19 33 30.4252 expand
20 34 30.4252 reflect
21 36 27.782 reflect
22 37 27.782 reflect
23 39 27.782 contract inside
24 41 22.6509 reflect
25 42 22.6509 reflect
26 43 22.6509 reflect
27 44 22.6509 reflect
28 45 22.6509 reflect
29 47 21.0211 reflect
30 48 21.0211 reflect
31 49 21.0211 reflect
32 51 21.0211 contract inside
33 52 21.0211 reflect
34 54 20.7613 contract inside
35 55 20.7613 reflect
36 56 20.7613 reflect
37 57 20.7613 reflect
38 59 20.6012 contract inside
39 61 20.5324 contract inside
40 63 20.4961 contract inside
41 65 20.3886 contract inside
42 67 20.2121 reflect
43 69 20.0876 contract inside
44 71 19.9164 reflect
45 72 19.9164 reflect
46 74 19.9164 contract inside
47 76 19.9164 contract outside
48 78 19.3349 expand
49 80 19.3349 contract inside
50 81 19.3349 reflect
51 82 19.3349 reflect
52 84 18.8721 expand
53 85 18.8721 reflect
54 87 18.6427 expand
55 89 17.4548 expand
56 90 17.4548 reflect
57 92 16.0113 expand
58 93 16.0113 reflect
59 94 16.0113 reflect
60 96 14.6134 expand
61 98 12.5445 expand
62 99 12.5445 reflect
63 101 10.7311 expand
Exiting: Maximum number of function evaluations has been exceeded
- increase MaxFunEvals option.
Current function value: 10.731146
xsol =
1.7022 1.0787 1.2034 0.5006 0.64666
</pre><h2>Exactly fix one variable, constrain some others, and set a tolerance<a name="7"></a></h2><pre class="codeinput">opts = optimset(<span class="string">'fminsearch'</span>);
opts.TolFun = 1.e-12;
LB = [-inf 2 1 -10];
UB = [ inf inf 1 inf];
xsol = fminsearchbnd(@(x) norm(x),[1 3 1 1],LB,UB,opts)
</pre><pre class="codeoutput">
xsol =
-4.9034e-07 2 1 5.1394e-07
</pre><h2>All the standard outputs from fminsearch are still returned<a name="8"></a></h2><pre class="codeinput">[xsol,fval,exitflag,output] = fminsearchbnd(@(x) norm(x),[1 3 1 1],LB,UB)
</pre><pre class="codeoutput">
xsol =
3.1094e-05 2 1 -5.1706e-05
fval =
2.2361
exitflag =
1
output =
iterations: 77
funcCount: 138
algorithm: 'Nelder-Mead simplex direct search'
message: [1x194 char]
</pre><p class="footer"><br>
Published with MATLAB&reg; 7.0.1<br></p>
<!--
##### SOURCE BEGIN #####
%% Optimization of a simple (Rosenbrock) function, with no constraints
rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;
% With no constraints, operation simply passes through
% directly to fminsearch. The solution should be [1 1]
xsol = fminsearchbnd(rosen,[3 3])
%% Only lower bound constraints
xsol = fminsearchbnd(rosen,[3 3],[2 2])
%% Only upper bound constraints
xsol = fminsearchbnd(rosen,[-5 -5],[],[0 0])
%% Dual constraints
xsol = fminsearchbnd(rosen,[2.5 2.5],[2 2],[3 3])
%% Mixed constraints
xsol = fminsearchbnd(rosen,[0 0],[2 -inf],[inf 3])
%% Provide your own fminsearch options
opts = optimset('fminsearch');
opts.Display = 'iter';
opts.TolX = 1.e-12;
opts.MaxFunEvals = 100;
n = [10,5];
H = randn(n);
H=H'*H;
Quadraticfun = @(x) x*H*x';
% Global minimizer is at [0 0 0 0 0].
% Set all lower bound constraints, all of which will
% be active in this test.
LB = [.5 .5 .5 .5 .5];
xsol = fminsearchbnd(Quadraticfun,[1 2 3 4 5],LB,[],opts)
%% Exactly fix one variable, constrain some others, and set a tolerance
opts = optimset('fminsearch');
opts.TolFun = 1.e-12;
LB = [-inf 2 1 -10];
UB = [ inf inf 1 inf];
xsol = fminsearchbnd(@(x) norm(x),[1 3 1 1],LB,UB,opts)
%% All the standard outputs from fminsearch are still returned
[xsol,fval,exitflag,output] = fminsearchbnd(@(x) norm(x),[1 3 1 1],LB,UB)
##### SOURCE END #####
-->
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