Network environment:

Https Client<=============>Proxy Server<==============>Https Server
                                                  192.168.17.11<-----extranet------>192.168.17.22
10.100.21.10<----intranet----->10.100.21.11

ps: Http Client without default gateway, but it can ping to 10.100.21.11

Description:

OS: Ubuntu 12.04 on 3 hosts
Https Client: Implement with java(openjdk-6).Have one network-interface.
Proxy Server: Apache2.2.Have two network-interfaces.
Https Server: Tomcat6.Have one network-interface.

I use two method to implement httpsurlconnection through proxy:
(For facilitate I do not write down about ssl handle function for checking serverTrusted and hostnameVerifier issue.If need I will update.)

1.Proxy class

InetSocketAddress proxyInet = new InetSocketAddress("10.100.21.11",80);
Proxy proxy = new Proxy(Proxy.Type.HTTP, proxyInet);
URL httpsUrl = new URL("https://192.168.17.22:8443/test");
HttpsURLConnection httpsCon = (HttpsURLConnection) httpsUrl.openConnection(proxy);

httpsCon.setDoOutput(true);
httpsCon.setDoInput(true);
httpsCon.setRequestMethod("POST");
OutputStream out = httpsCon.getOutputStream();
OutputStreamWriter owriter = new OutputStreamWriter(out);

owriter.write("<request>test</request>");
owriter.flush();
owriter.close();
...

This method workable and I observed packets flow also met my expectation.
HttpClient ---> ProxyServer ---> HttpServer

But when I use set Property method:

2.setProperty

System.setProperty("http.proxySet", "true");
System.setProperty("http.proxyHost",10.100.21.11);
System.setProperty("http.proxyPort","80");

URL httpsUrl = new URL("https://192.168.17.22:8443/test");
HttpsURLConnection httpsCon = (HttpsURLConnection)httpsUrl.openConnection();

httpsCon.setDoOutput(true);
httpsCon.setDoInput(true);
httpsCon.setRequestMethod("POST");
OutputStream out = httpsCon.getOutputStream();
OutputStreamWriter owriter = new OutputStreamWriter(out);

owriter.write("<request>test</request>");
owriter.flush();
owriter.close();
...

I got a NoRouteToHostException: Network is unreachable.
It make me confused.I did not see any packets between HttpClient and ProxyServer.
But HttpClient can ping to ProxyServer(10.100.12.10 ping 10.100.21.11)

So I remove proxy setting(as without using proxy):
Also got NoRouteToHostException: Network is unreachable.
I thought this is reasonable.Because there is no route to extranet.

I guess it seems like to setProperty method that the inner function of httpsUrlConnection will to check this url can be reachable or not.

But it is weird. 1st method can be success.

Have any idea? Or what are different between 1st and 2nd method?

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Update

System.setProperty("https.proxyHost",10.100.21.11);
System.setProperty("https.proxyPort","80"); 

It can work and packets flow are correct what I expect for.
But set https.proxyPort=443 is not workable for me

System.setProperty("https.proxyPort","443");

It will thorow a exception as bellow:

java.net.SocketException: Unexpected end of file from server 
at sun.net.www.http.HttpClient.parseHTTPHeader(HttpClient.java:770)
....

So I thought Apache Proxy have also to be modified to the right configuration.

Your URL connection is https whereas you are only setting the http proxy.

Try setting the https proxy.

//System.setProperty("https.proxySet", "true"); 
 System.setProperty("https.proxyHost",10.100.21.11);
 System.setProperty("https.proxyPort","443");

EDIT @EJP is correct. There is no https.proxySet .. I copied your original question and included in the answer.