Keeping mandarinfish alive in a closed system (aquarium) for any length of time has always been a problem for aquarists. It used to be thought that if a mandarin was placed in a tank with a ton of live rock that the fish would be able to thrive on the (supposedly) huge amount of copepods that populate the live rock. Unfortunately, this has not proved to be the case in most instances. Before long, the mandarins would consume the copepod population and then slowly starve to death. For mandarinfish to survive in an aquarium, they must be "trained" to consume high quality, high protein foods that are readily available.
Several aquarists have been experimenting with different methods to wean mandarins off of live food (copepods) and onto frozen Mysis shrimp, which fulfills all of the mandarin's nutritional needs and then onto pelletized foods. One successful method was to place the new mandarins in a breeding basket or small Q.T. tank and feed them live brine shrimp, which they will normally take to quite well (the live shrimp's movement makes it very tantalizing), then slowly start adding a few frozen Mysis shrimp to the basket or Q.T. tank. Over time, and with some luck, the mandarins will start tasting the Mysis shrimp and accepting it as food. Once the mandarins have been weaned off of the live brine shrimp, they can then be safely moved to the display tank and fed only Mysis shrimp.
Keep in mind, however, that the mandarin will never be a voracious eater and will therefore never be able to compete with more aggressive feeders in an aquarium, so their tankmates must be carefully chosen.
From personal experience, we have found that many of the mandarins that we have weaned onto Mysis shrimp will actually wait for the eyedropper with Mysis shrimp in it to appear at the edge of the tank and then literally suck the shrimp out of the eyedropper.