Neither example sentence (is/are) is right...
Using this method and applying the mentioned principles is able to improve the performance. *
no
Using this method and applying the mentioned principles are able to improve the performance. *
no
There are different ways to fix this. One is to add a subject:
Using this method and applying the mentioned principles, engineers are able to improve performance.
ok
Using this method and applying the mentioned principles, one is able to improve performance.
ok
Or, you may change the format of the sentence slightly:
Using this method and applying the mentioned principles allows performance to be improved.
or
Using this method and applying the mentioned principles leads to improved performance.
This last sentence with "leads" as the verb has the original problem you asked about: Should the verb be singular or plural?
While either of those choices could be within the realm of possibility, the singular flows better, and seems to be preferable. So you'd understand it this way:
(Using this method and applying the mentioned principles) leads to improved performance.