This monograph deals with the general principles of the theory of extremal problems. In particular, the author discusses Lagrange's principle, the duality principle, the complete elimination of restrictions, the Hamilton-Jacobi principle, the extension of extremal problems, and the invariance principle. These principles enable a variety of different extremal problems (for example, the calculus of variations, optimal control, and convex programming), to be considered from a unified point of view.

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