MinOrDefault extension is not supported

I just would like to confirm that

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Collection.Min(p => p.Value); 

Works only if the Collection is not empty and there is no MinOrEmpty or something similar, right ?

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If you want it to return the default value for the element type if it's empty, that's easy:

var min = Collection.Select(p => p.Value).DefaultIfEmpty().Min();

Alternatively, if you want a particular minimum value:

var min = Collection.Select(p => p.Value)
                    .Concat(Enumerable.Repeat(int.Minvalue, 1)
                    .Min();

Or:

var min = Collection.Select(p => (int?) p.Value)
                    .Min(); // min will be the null value if Collection is empty

Is that what you're after? It's not entirely clear.

Min and Max behave slightly differently for empty sequences of non-nullable element types than for empty sequences of nullable element types. When the element type is nullable, the null value is returned if and only if the sequence is empty; for non-nullable element types, InvalidOperationException is thrown. See my Edulinq blog post on Min/Max for more details.

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If the collection contains nullable types -- either reference types or Nullable<T> values -- then the Min method will return null if the collection is empty.

If the collection contains non-nullable value types then the Min method will throw an InvalidOperationException if the collection is empty.

Note that in your example, where you're passing a delegate to the Min method, then the behaviour is determined by the delegate's return type, not the type of the elements themselves.

(And no, there's no built-in MinOrEmpty method. There are plenty of easy alternatives though, see Jon's answer for details.)

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If the sequence is empty is does not make sense to compute the minimum value. However, if you want to return a specific value if the sequence is empty you can do it like this (assuming that your a computing the minimum of int values):

int defaultMinValue = -1;
var min = Collection.Select(p => p.Value).DefaultIfEmpty(defaultMinValue).Min();

If the sequence is empty it will return -1, otherwise it will compute the the minimum value of the sequence.