Programmatically switching off Android phone

As CommonsWare already said that this is not possible in an Ordinary SDK Application. You need to sign your app with the System Firmware Key. But it's possible for your app with Root privileges. Try using the following code (if you have SU access):

Shutdown:

try {
    Process proc = Runtime.getRuntime()
                    .exec(new String[]{ "su", "-c", "reboot -p" });
    proc.waitFor();
} catch (Exception ex) {
    ex.printStackTrace();
}

Restart:

Same code, just use "reboot" instead of "reboot -p".

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[On an other note: I read somewhere that these commands do not work on Stock HTC ROMs, but haven't confirmed myself]

You cannot do this from an ordinary SDK application. Only applications signed with the system firmware signing key can do this.