Proxy preferences for Eclipse applications are stored in the file
<eclipse-installation>/configuration/.settings/org.eclipse.core.net.prefs
So either you edit the settings via the Eclipse preferences UI (General / Network Connections) and then copy that file to your headless application, or you create/edit that manually:
eclipse.preferences.version=1
nonProxiedHosts=localhost|127.0.0.1
org.eclipse.core.net.hasMigrated=true
proxiesEnabled=true
proxyData/HTTP/hasAuth=false
proxyData/HTTP/host=<proxy.your.org>
proxyData/HTTP/port=<port>
proxyData/HTTPS/hasAuth=false
proxyData/HTTPS/host=<proxy.your.org>
proxyData/HTTPS/port=<port>
# - Set SOCKS proxy only if neccessary -
# proxyData/SOCKS/hasAuth=false
# proxyData/SOCKS/host=<proxy.your.org>
# proxyData/SOCKS/port=<port>
systemProxiesEnabled=false
HTH.