Apart of the VARIADIC option pointed by @a_horse_with_no_name, which is only a syntax sugar for passing an array with any number of elements of the same type, you can't define a function with optional parameters because, in postgres, functions are identified not only by its name but also by its arguments and the types of them.
That is: create function foo (int) [...]
and create function foo (varchar) [...]
will create different functions.
Which is called when you execute, for example, select foo(bar)
depends on bar data type itself. That is: if it is an integer, you will call the first one and if it is varchar, then second one will be called.
More than that: if you execute, for example, select foo(now())
, then a function not exists exception will be triggered.
So, as I said, you can't implement functions with variable arguments, but you can implement multiple functions with the same name and distinct argument (an/or type) sets returning the same data type.
If you (obviously) doesn't want to implement the function twice, the only thing you need to do is to implement a "master" function with all possible parameters and the others (which have fewer parameters) only calling the "master" one with default values for the non received parameters.