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Marcel Kronfeld
2007-12-11 16:38:11 +00:00
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<html>
<head>
<title>f_1 : Sphere function</title>
</head>
<body><EFBFBD>
<h1 align="center">The Sphere function</h1>
<center>
<img src="images/f1tex.jpg" width="85" height="95" border="0" align="center">
</center><br>
The sphere function is a <i>n</i>-dimensional, axis-symmetric, continuously differentiable, convex function:
<p>
Because of its simplicity every optimization-algorithm should be able to find its global minimum at <i>x</i>=[0, 0, ... , 0]
<p>
<img src="images/f1.jpg" width="480" height="360" border="2" align="middle">
<hr>
More information about the sphere function can be found at:
<p>
Kenneth De Jong. <i>An analysis of the behaviour of a class of genetic adaptive systems.</i> Dissertation, University of Michigan, 1975. Diss. Abstr. Int. 36(10), 5140B, University Microflims No. 76-9381.
</body>
</html>