Smirnov V.I.'s A course of higher mathematics, vol. 1 PDF

By Smirnov V.I.

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Gr By means of the tools developed in Chapter IV we will be able to give conditions which ensure that the problem (23) optimal production plan is solvable. - (25) of finding an We shall also demonstrate that there is then an optimal production plan involving at most n activities. This result is true even if there are arbitrarily many possible activities. The study of production models of the same kind as, and similar to, that of problem (23) - (25) has greatly stimulated the development of The whole theory of Chapter IV as well as the simplex linear programming.

31 State Diagrams and Duality Gaps By the same token, the dual problem must be in one and only one of the three states indicated below. ) The statement of the duality theorem (18) of §4 may be represented by the state diagram below. Combinations of states of the dual pair (P) - (D) which are impossible by (18) of §4 are marked with a cross in the diagram. ) State diag ram for the dual pair (P) (1) - (D). P D IC B UB IC 1 2 4 B 3 5 x UB 6 x x The Case 5 is of main interest for the applications. are both bounded.

G. Gorr, Gustafson and Kortanek (1972) and Gustafson and Kortanek (1975). Chapter II Weak Duality The present chapter is very elementary in its entirety but is of decisive importance for understanding the material to follow. Here we lay the foundations for the theoretical as well as computational treatment of linear optimization problems. The simple examples are particu- larly designed in order to familiarize the reader with the structure of such problems as well as the central concept of duality which plays a major role both in the theory and in all practical applications of linear optimization.

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A course of higher mathematics, vol. 1 by Smirnov V.I.

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