A theorem in convex programming

William Karush

Naval Research Logistics Quarterly, 1959, vol. 6, issue 3, 245-260

Abstract: An optimization problem which frequently arises in applications of mathematical programming is the following: Where fi are convex functions. In this paper, the function F is studied and shown to satisfy F(A, B) = M (A) + N(B), where M and N are increasing and decreasing convex functions, respectively. Also, the functional equation F (A, C) = F(A, B) + F(B, C) − F(B, B) is established. These results generalize to the continuous case F(A, B)=min ∫ OT f(t, x(t))dt, with x(t) increasing and A ≤ x (0) ≤ x (T) ≤ B. The results obtained in this paper are useful for reducing an optimization problem with many variables to one with fewer variables.

Date: 1959
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:6:y:1959:i:3:p:245-260

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