Extremum theory and external problems of the classical calculus (Q5948391)

In this well-written self-contained paper (references are made only to the well-known facts from university courses) the author formulates main questions that are essential in the theory of extremum problems. Namely, questions about existence, necessary and sufficient conditions of optimality, possibility of finding a solution explicitely and the question about behaviour of optimal solution under perturbations. Further, he presents fundamental principles (e.g., Lagrange principle) and techniques with the help of which answers to posed questions are possible to get. Several problems related to classical calculus of variations are analysed in detail.