It is not possible without letting the network down and up at the client network interface.
Theoretically, the DHCP server can send a FORCERENEW message to all connected clients. FORCERENEW is described at RFC3203. (See also https://serverfault.com/a/569869/107832)
Unfortunately, the famous ISC DHCP Server does not support it:
- no current plans for RFC3203 support, also because of the lack of support for 3118 authentication
- no real interested by users
RFC 3315 states in section 19.4.1 reconfigure messages. This is, however, for IPv6 only. A message states that DOCSIS 3.0 “requires Reconfigure support (for DHCPv6) as specified in RFC3315”