A Comparative Study of Solutions to the Holt Modigliani Muth And Simon Disaggr
A Comparative Study of Solutions to the Holt Modigliani Muth And Simon Disaggr
Dan I Candea
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L. Given a certain aggregate inventory Iq the problem is that of finding the root of an equation. However, it is easy to transform this root-finding problem into a maximization/minimization which has the advantage that some of the many optimum seeking methods available in the literature could be applyed to obtain the solution A . Let : I* (7) (8) It is obvious that a solution to (4) is obtained when VJ/(A)=0, which is equivalent to minimizing f ( A ) . Fig. 3 shows the relationship among Iq(A),... ^ (A), and f (A) . Thusour problem is now one of unconstrained optimization (minimization), iM'i:=^^' a) b) c) Fig. 5 - 10 - 3. METHODS FUR UNCONSTRAINED OPTIMIZATION - A REVIEW - 3. 1. Several variables problems The literature oresents a large set of optimum seeking methods for multivariate problems /lO/, /ll/, /6/, /7/. Fletcher in /6/ groups these methods in 3 broad catego- ries, according to their basic principle : gradient methods, direct senrch, and sums of squares. The problem to be considered is that of finding a local minimum (or if the function is uni- modal the global minimum) of a function f(x) where x is a vector of n variables x=(x, jXp, .
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