By Vinogradov V.
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Explains easy methods to elevate the modularity, flexibility, and maintainability of your SAS code utilizing the SAS macro facility. offers whole information regarding macro language components, interfaces among the SAS macro facility and different components of SAS software program, and macro processing ordinarily.
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Additional resources for A cookbook of mathematics
Xn , λ1 , . . , λm ) = f (x1 , . . , xn ) + j=1 where λ1 , λ2 , . . , λm are constant (Lagrange multipliers). Recipe 13 – What are the Necessary Conditions for the Solution of (4)? Equate all partials of L with respect to x1 , . . , xn , λ1 , . . , λm to zero: m ∂L(x1 , . . , xn , λ1 , . . , λm ) ∂f (x1 , . . , xn ) ∂g j (x1 , . . , xn ) = − λj = 0, ∂xi ∂xi ∂xi j=1 ∂L(x1 , . . , xn , λ1 , . . , λm ) = bj − g j (x1 , . . , xn ) = 0, ∂λj i = 1, 2, . . , n, j = 1, 2, . . , m. Solve these equations for x1 , .
X1 ≥ 0, . . , xn ≥ 0 (6) i Similarly, the minimization problem is min f (x1 , . . , xn ) subject to g (x1 , . . , xn ) ≥ bi , i = 1, 2, . . , m. x1 ≥ 0, . . , xn ≥ 0 i First, note that there are no restrictions on the relative size of m and n, unlike the case of equality constraints. Second, note that the direction of the inequalities (≤ or ≥) at the constraints is only a convention, because the inequality g i ≤ bi can be easily converted to the ≥ inequality by multiplying it by –1, yielding −g i ≥ −bi .
M ) which satisfies Kuhn-Tucker necessary conditions and for which L(x, λ∗ ) ≤ L(x∗ , λ∗ ) ≤ L(x∗ , λ) for all x = (x1 , . . , xn ) ≥ 0, λ = (λ1 , . . , λm ) ≥ 0 is known as the saddle point problem. Proposition 31 If (x∗ , λ∗ ) solves the saddle point problem then (x∗ , λ∗ ) solves the problem (6). 51 Economics Application 7 (Economic Interpretation of a Nonlinear Program and KuhnTucker Conditions) A nonlinear program can be interpreted much like a linear program. A maximization program in the general form, for example, is the production problem facing a firm which has to produce n goods such that it maximizes its revenue subject to m resource (factor) constraints.