Is this Boost Converter okay?
Capacitor would discharge, but not immediately. If your frequency is high enough and duty cycle is right, it will remain charged. 

The operation is very simple and is based on two basic properties: inductor's current can't change immediately and capacitor voltage can't change immediately. So you charge your inductor by closing the switch, the open it and current flows to capacitor and load. Since the frequency is high, voltage on the capacitor doesn't change. 

With you values you will have to go to quite high frequency...