Get minvalue of a Map(Key,Double)

You can use the standard Collections#min() for this.

Map<String, Double> map = new HashMap<String, Double>();
map.put("1.1", 1.1);
map.put("0.1", 0.1);
map.put("2.1", 2.1);

Double min = Collections.min(map.values());
System.out.println(min); // 0.1

Update: since you need the key as well, well, I don’t see ways in Collections or Google Collections2 API since a Map is not a Collection. The Maps#filterEntries() is also not really useful, since you only know the actual result at end of iteration.

Most straightforward solution would then be this:

Entry<String, Double> min = null;
for (Entry<String, Double> entry : map.entrySet()) {
    if (min == null || min.getValue() > entry.getValue()) {
        min = entry;
    }
}

System.out.println(min.getKey()); // 0.1

(nullcheck on min left aside)