It is known that re-using oneself idea in his/her published work without citing is considered self-plagiarism. In school, submitting an assignment which uses certain amount of works from a previously submitted assignment without mentioning it properly can be considered self-plagiarism. If one submits a research proposal which contains original research idea, and later proposed another proposal (let's say, for applying graduate school)containing significant parts of ideas from the previous one without mentioning it, can this be considered as self-plagiarism?
Is re-using an idea from a research proposal considered as self-plagiarism?
No: You can re-use ideas from research proposals which you haven't executed upon, i.e., ideas that you haven't advanced (e.g., because the research proposal was rejected or that part of the proposal was never addressed or ...), they're still fresh ideas.