# Control Theory and Optimization I: Homogeneous Spaces and by M.I. Zelikin, S.A. Vakhrameev

By M.I. Zelikin, S.A. Vakhrameev

The single monograph at the subject, this ebook matters geometric equipment within the idea of differential equations with quadratic right-hand aspects, heavily with regards to the calculus of adaptations and optimum regulate idea. in line with the author’s lectures, the booklet is addressed to undergraduate and graduate scholars, and medical researchers.

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**Additional resources for Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Encyclopaedia of Mathematical Sciences) **

**Sample text**

When this is the case, the average holding plus fixed order costs per unit time as a function of the vector x, denoted as AC(x), may be written as S j ∈J Dj xj Hb + . 17) AC(x) = b 2 Finding the best solution of this type then requires solving the following problem: n rj − Maximize j =1 S Hb Dj xj − b 2 Subject to xj ∈ {0, 1}, j = 1, . . , n. 19) The above problem is easily solved by inspection by setting xj = 1 for each demand j such that rj > S/b (interestingly, this solution may also be obtained exactly as before: by sorting demands in nonincreasing order of unit revenue values and evaluating all solutions of the form xj = 1 for j = 1, .

Production in any period carries a fixed order cost as well as variable production costs, and inventory may be held from period to period, incurring an associated holding cost. The planner’s goal is to maximize profit from order acceptance decisions over the planning horizon. 1 Demand Selection Problem Definition The model we consider in this chapter generalizes the ELSP, discussed in Chap. 1, and is intimately related to the ELSP with pricing presented in Chap. 2, as we later discuss in Sect. 4.

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