论文信息 - the Method of Tents in the Theory of Extremal Problems

the Method of Tents in the Theory of Extremal Problems

The method of tents is a unified method of solving various kinds of extremal problems. It is a development of the method of Milyutin and Dubovitskii, but it removes their restrictive assumption that certain cones must be solid. The present exposition is limited to the finite-dimensional case. As applications, we give detailed proofs of very general necessary conditions for various types of extremal problems, such as the problems of mathematical programming, of optimal control (in particular, we include a proof of Pontryagin's maximum principle), and of minimax problems.

V G Bolt'yanskii | V. G. Bolt'yanskii

[1] V. G. Boltyanskiy. The Maximum Principle in the Theory of Optimal Processes. , 1961 .

[2] Lucien W. Neustadt,et al. An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems. I. General Theory , 1966 .

[3] Maximum principle for differential inclusions (necessity) , 1971 .

[4] H. Halkin. A Maximum Principle of the Pontryagin Type for Systems Described by Nonlinear Difference Equations , 1966 .

[5] R. V. Gamkrelidze,et al. On the Theory of Optimal Processes in Linear Systems , 1961 .

[6] E. Polak,et al. Constrained Minimization Problems in Finite-Dimensional Spaces , 1966 .

[7] B. W. Jordan,et al. Theory of a Class of Discrete Optimal Control Systems , 1964 .

[8] L. T. Fan,et al. The Discrete Maximum Principle: A Study of Multistage Systems Optimization , 1964 .

[9] R. Bellman. Dynamic programming. , 1957, Science.

[10] H. Halkin,et al. Discretional Convexity and the Maximum Principle for Discrete Systems , 1966 .

[11] L. Bittner. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishechenko, The Mathematical Theory of Optimal Processes. VIII + 360 S. New York/London 1962. John Wiley & Sons. Preis 90/– , 1963 .

[12] A maximum principle for differential inclusions , 1970 .